Consumer Math 30S
Probability Unit
Topics:
•
•
•
•
•
Introduction to Probability
Expressing Probabilities
Making Predictions Using Probability
Comparing Probability and Odds
Expected Value
Consumer Math 305
Probability Unit
What is Probability?
Probability is an important branch of mathematics. It is one of the branches that is extremely relevant in
your everyday life. Many decisions in your life involve probability. An understanding of probability will help
you in making informed and responsible decisions.
Probability is concerned with the likelihood of events occurring. Problems that involve probability are
discussed in Lessons 1 and 2. Probability is not the only way to express the likelihood of events occurring.
The likelihood of events occurring can also be expressed in terms of odds. Lesson 3 discusses the
similarities and differences between probability and odds, Another application of probability, expected
value, is discussed in Lessons 4 and 5. Expected value is an application of probability that involves the
likelihood of gain or loss.
Lesson 1 - Introduction to Probability
When you complete this lesson, you will be able to
•
represent the probability of an event on a probability scale, express the probability of an event as a
ratio, a fraction, a decimal, and a percent.
Probability involves the likelihood of events occurring. The probability of an individual event occurring can
be represented on a probability scale as follows.
impossible
less likely
more likely
certain
Mathematically, probability is defined as follows.
Probability of an event =
number of ways the event can occur
total number of possible events
Since the number of ways an event can occur is always less than or equal to the total number of possible
events, the probability is always a numerical value between 0 and 1.
The less likely an event is to occur, the closer its probability will be to O.
The more likely an event is to occur, the closer its probability is to 1.
A probability of 0 indicates that the event is an impossibility, while a probability of 1 indicates it is a
certainty.
Example 1
Place the following events on a probability scale.
a.
The sun will rise in the east next Sunday.
impossible
less likely
more likely
certain
Consumer Math 30S
Probability Unit
Example 1 Continued...
b.
The next baby born in your local hospital will be a boy.
impossible
c.
less likely
more likely
certain
Somewhere in Manitoba, the temperature will reach at least 4° C once next year during the month
of January.
impossible
less likely
more likely
certain
Since an event has to either occur or not occur, the probability of an event occurring plus the probability of
an event not occurring is a certainty and equal to 1.
Therefore, if you know the probability of an event occurring, you can subtract this probability from 1 to find
the probability of it not occurring.
Example 2
If the probability of an event occurring is 1/3, the probability of it not occurring is 1 - 1/3 = 2/3.
Example 3
Express the probability of a single coin landing "heads" in the following ways.
a.
a fraction
a ratio
c.
a decimal
d.
in words
-2-
Consumer Math 30S
Probability Unit
Assignment 1 — Introduction to Probability
1.
Place the following events on a probability scale.
a.
You will live for 100 years.
impossible
more likely
less likely
certain
In the first week of November, it will snow at least once in Thompson, Manitoba.
b.
impossible
c.
less likely
more likely
certain
more likely
certain
more likely
certain
The sun will rise in the west tomorrow.
impossible
d.
less likely
The next baby born in your local hospital will be a girl.
impossible
less likely
2.
Rewrite each of the following statements without using the words "chance", "probability", or
"likelihood".
a.
The probability of team A winning the baseball game on Saturday is 0.8.
b.
There is a 50% chance of rain on Monday.
c.
The probability of a person living to age 90 is 0.02.
3.
The probability scale is marked from the impossible to the certain. Write a decimal to represent the
probability of an event occurring at each of the points A, B, C, D, and E.
A
-3-
Consumer Math 30S
Probability Unit
4.
People often use the phrase "one chance in a million."
Write this probability as a decimal and as a percent.
5.
It is often difficult to picture or have a sense of a very large number. One way of thinking about a
million is the following. There are about 100 000 words in a good-sized novel. Therefore, 10 goodsized novels contain about 1 000 000 words. How can you picture a one-in-a-million chance in
terms of this representation of a million?
6.
Consider the following three statements made by a salesperson to promote a product.
•
•
It is effective 99% of the time.
There is a one-in-a-million chance it won't be effective. It usually is effective.
Do all these statements mean the same thing? Explain.
7.
If you were told that the probability of an airplane crashing on any flight is 0.005, would you
consider this to be an acceptable level of probability? Explain.
8
The probability of winning a particular 6-49 lottery is approximately 1 in 14 000 000. The probability
of being hit by lightning once in your lifetime is approximately 1 in 600 000.
a.
Are you more likely to win the 6-49 lottery or to be hit by lightning?
b.
How much more likely is one than the other?
-4-
Consumer Math 305
Probability Unit
Lesson 2— Expressing Probabilities
Probability is an indication of the likelihood of an event occurring. It is expressed as a comparison of
desired outcomes to total outcomes. Probabilities can be expressed in different ways (fractions, decimals,
percents, and words).
Example 1
Some people say there is "one chance in ten" and other people say there is a 1/10 chance. Both mean the
same thing.
Example 2
There are 13 spades in a deck of 52 cards. This can be expressed in the following ways:
fraction
decimal
percent
in words
-5-
Consumer Math 30S
Probability Unit
Lesson 2 Assignment — Expressing Probabilities
Complete the following chart, which shows different ways to express a probability.
Fraction
Decimal
Percent
C.42_
Words
one in five
to
IA
(..) i t- '
0.3
A
-....
60%
OW
9
2.
Complete the chart below. It shows the probability of randomly selecting a student with a particular
hair colour from the population of a high school.
Colour
Decimal
Bro
Percent
Fraction
Words
five out of ten
Sc
Blonde
Black
Red
1/8
0.25
5%
Other
seventy-five out of 1000
33ic
3.
When rolling a fair six-sided die, express the probability that:
a)
you will roll a 2; express this as a fraction
b)
you will roll a prime number; express this as a fraction
c)
you will roll a 3 or a 4; express as a percent
tr,
d)
_
you will roll a seven, express in words
-6-
I)
3
Consumer Math 30S
Probabitity Unit
4.
You are tossing two coins and want to get two "heads'. Draw a tree diagram and then state the
probability of this happening as a:
a)
decimal
b)
fraction
c)
percent
d)
word phrase
t
CTIA-Q
5.
You are rolling two dice and want a pair of threes. State the probability of this happening as a:
a)
decimal
o2
'1
(
)
3(0
)4-SS
63
b)
fraction
percent
d)
,78
word phrase
-7-
ev%Sc ‘-st.
LA
Yee S
(
S5t
Consumer Math 308
Probability thrt
6.
You open a standard deck of playing cards.
a)
How many cards are in the deck?
b)
How many clubs, spades, diamonds, and hearts are there?
13i/a
c)
How many red, black cards are there?
How many face cards (Jack, Queen, King) are there?
1 /4(
e)
How many numbers are there?
When drawing a card randomly from a standard deck of playing cards, what is the probability it will
be a:
a)
heart
b)
red card
c)
5
d)
face card (Jack, Queen, or King)
e)
black 6
-8-
Consumer Math 30S
Probability Unit
8.
If each month is equally likely, determine the probability of being born in a particular month.
Express this probability as a fraction, a percent, and in words.
9.
You are tossing three coins and want to get three "heads". Draw a tree diagram and then state the
probability of this happening as a:
10.
a)
decimal
b)
fraction
c)
percent
d)
word phrase
When buying a box of 30 Christmas oranges, you can expect 10% of the oranges to be rotten. If
you pick an orange at random, state the probability that you will pick:
a)
a rotten orange
b)
a good orange
Consumer Math 303
Probability Unit
Lesson 3 — Making Predictions Using Probability
We can use probability to predict answers to questions. If our samples are random, or fairly chosen, we can
use these probabilities to make predictions.
When you complete this lesson, you will be able to solve a variety of problems involving probability.
Example 1
If there is a probability that one person in seven has green eyes, how many in a group of 210 are likely to
have green eyes?
green eyes
sample size
r
green eyes in group
total in group
Example 2
In a pack of 20 wolves, 9 had frost damage to their ears, and 11 did not. If there are an estimated 610
wolves in the southern Yukon, how many do you predict will have frost-damaged ears?
damaged ears =
sample size
damaged ears
total estimated population
Example 3
You enter a store promising to award 10 door prizes per day. It is near closing time, and they have awarded
6 gifts so far. If there are 200 people in the store, what is the probability of you receiving a door prize?
3
-10-
Consumer Math 30S
Probability Unit
Example 4
A city is interested in knowing how many of its roads and sidewalks need to be repaired. A city engineer
randomly inspects 38 city roads and finds four that need to be repaired. He also finds that six of the 45 city
sidewalks he inspects need to be repaired.
a.
What is the probability a city road has to be repaired? Express this probability as a decimal.
OS
b.
What is the probability a city sidewalk has to be repaired? Express this probability as a decimal.
Cl
c.
33
/33
How do the roads and sidewalks of the city compare in this respect?
Example 5
During the regular playing season, 10 out of 84 games in a particular soccer league go into overtime.
a.
What is the probability that a particular game will go into overtime?
c
b.
Based on this probability, how many of the league's 16 playoff games will go into overtime?
£
c.
I/
C/n--e CJ
/i /
Would you expect the probability of playoff games going into overtime to be the same as regular
season games? Explain.
I.
Consumer Math 30S
Probability Unit
Assignment 3 — Making Predictions Using Probability
The probability of experiencing a mechanical breakdown on the highway is one in seventy. If 3500
cars are travelling down the highway, how many do you predict will have a mechanical breakdown?
')/
2.
Harry's Chevrolet-Buick in Burnaby plans to se
an 900 of them will have
standard transmissions. Find the probability that the next car sold will have a standard
transmission.
3 2 c)
3.
Danny's Disc Depot sold 1850 CDs over the holiday season. Thirty-seven were returned with
defects. Using this data, what is the probability that any given customer purchased a defective CD?
0 2_
4.
A video rental shop is holding a clearance sale on previously rented DVDs. The probability of a
DVD being flawed is 3 in 100. The store has already sold 239 DVDs and non have been flawed.
Based on probability, how many of these would you expect to be flawed?
(71
-)(
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Consumer Math 30S
Probability Unit
5.
During a municipal election, 308 voters are registered at one polling station and 272 voters are
registered at a second polling station. At the first polling station 148 voters cast their ballots. At the
second polling station 131 voters cast their ballots.
a.
What is the probability voters at the first polling station cast their ballots? Express this probability as
a percent.
jt
3eS"
b.
oitg o 5
LW, i
What is the probability voters at the second polling station cast their ballots? Express this
probability as a percent.
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9,,TL
d.
At which polling station were the voters more likely to cast their ballots?
6.
A batting average is expressed as a number to three decimal places. A player's batting average is
the probability of the total number of hits compared to the total number of official times the player is
at bat. For example, if a batter has 15 hits in 60 official times at bat, his batting average would be
15 / 60 = .250.
a.
What is the batting average of player A who has 18 hits in 70 official times at bat?
s 70
b.
What is the batting average of player B who has six hits in 25 official times at bat?
O.
c.
2L1O
Which of the two players has the higher batting average?
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Consumer Math 30S
Probability Unit
d.
Explain what a batting average of .125 means.
e.
If a batter's average is .275, how many hits would you expect this batter to have in 100 official
times at bat?
100
7.
A coin is tossed 20 times.
a.
If it were to land on heads 11 times, would you believe it is a fair coin? Explain.
b.
If it were to land on heads 19 times, would you believe it is a fair coin? Explain.
c.
If it were to land on heads 15 times, would you believe it is a fair coin? Explain.
2
- 14 -
Consumer Math 30S
Probability Unit
8.
The probability a person is left-handed is 1 in 10. The city of Winnipeg has a population of
approximately 650 000 people.
a.
Approximately how many left-handed people live in Winnipeg?
/O
X
b.
If you were an entrepreneur and wanted to open a store carrying items for left-handed people, what
other information would help you decide if you should open such a store in Winnipeg?
9.
Canned Air offers its passengers a choice of two different types of meals on its dinner flights,
vegetarian lasagna or meat lasagna. On its flights last year, approximately 18 000 out of 30 000
passengers chose the meat lasagna.
a.
What is the probability of a particular passenger choosing the meat lasagna?
b.
Based on this probability, how many vegetarian lasagna meals should Canned Air order for a
dinner flight on which there are 228 passengers booked?
91,
9'
10.
2
2_,
vr,
The probability of twins being born is 1 : 90. If during one year there were 15 500 births in a
particular city, how many of these births would probably have been twins?
-15-
S
Consumer Math 308
Probability Unit
11
An entrepreneur determines that 2% of her business is lost due to bad debt. If she bills $68 500
during a year, approximately how much will she lose due to bad debt?
12.
If you are living in Canada at present, the probabilities for having a certain hair colour are given in
the following chart.
Colour
Ratio
Brown
7 : 10
Blonde
1: 7
Black
Red
1: 10
1:17
Decimal
%
a.
Express each of these probabilities as a decimal and a percent.
b.
In a class of 34 students, how many students would you expect to have red hair?
Consumer Math 303
Probability Unit
Lesson 4 - Comparing Probability and Odds
When you complete this lesson, you will be able to
• determine the odds in favour of an event occurring
• determine the odds against an event occurring
• understand the differences between probability and odds
The likelihood of an event occurring is not always expressed in terms of probability. The likelihood of an
event occurring can be expressed in terms of the "odds in favour" of it occurring. The odds of an event
happening are found by comparing the number of desired outcomes to the number of undesired outcomes,
which is different from finding probability.
Example 1
When rolling a six-sided die, determine the odds in favour of rolling a 4, How is this different from the
probability of rolling a 4?
Odds in favour =
favourable outcomes : unfavourable outcomes
ea
Probability
=
0 Fall 1;0
47- 1 r ?A
,4
e
number of desired outcomes
total possible outcomes
Example 2
When drawing a card from a well-shuffled deck of playing cards, determine the odds in favour of drawing a
diamond.
Odds in favour =
favourable outcomes : unfavourable outcomes
( 3
G 11
- d t
) et fri try\ olS
I
12S
141 e
S p et:
13
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• Consumer Math 30S
Probability Unit
Example 3
Roll a six-sided number cube and determine the following.
a.
SC
the probability of rolling a number less than three
61-4
b.
the odds of rolling a number less than three
c.
the odds against rolling a number less than three
Example 4
A wallet contains three $5.00 bills, two $10.00 bills, and one $20.00 bill. What are the odds against drawing
out a $10.00 bill?
Si 1-1-5
Odds against =
unfavourable outcomes : favourable outcomes
a re 410
awoo
iD
es2
2u
Example 5
A surve of 320 students in your school reveals that 240 of them listen to radio station CFAM. Find the odds
against randomly selecting a student who listens to this station.
Odds against =
unfavourable outcomes : favourable outcomes
- 18 -
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I/
s
012 tri
Consumer Math 30S
Probability Unit
Assignment 4— Comparing Probability and Odds
1.
Complete the following chart:
Event
drawing a queen from a
deck of cards
rolling a sum of 9 using
two dice
drawing a 3 of diamonds
from a deck of cards
choosing the letter "a"
from the word "aardvark"
rolling a sum greater
than 6 with 2 dice
drawing a black 4,6, or
8 from a deck of cards
rolling a sum of 2 with
two dice
-1
wï
J
probability
Odds against
Odds in favour
4,.
?
is
I
I
2.
Explain the difference between probability and odds.
3.
Each letter of the word MATHEMATICAL is on a different card. All the cards are the same size.
The cards are placed face down and shuffled.
Lc
a)
Determine the probability of drawing an M.
2
b)
Determine the odds in favour of drawing an M.
Cr;
r
Determine the probability of not drawing an M.
,
d)
Determine the odds against drawing an M.
-19-
Consumer Math 30S
Probability Unit
4.
Use the spinner shown here to answer the
questions that follow:
a)
What is the probability of spinning red?
b)
What are the odds in favour of spinning red?
c)
What is the probability of spinning yellow?
1
d)
5.
What are the odds against spinning yellow?
There are 4 white, 14 blue, and 5 green marbles in a bag. A marble is selected from the bag
without looking. Find the odds of the following:
a)
the odds against selecting a green marble
b)
the odds in favour of not selecting a green marble
c)
the odds in favour of the marble selected being either a white or a blue marble
What is true about the above odds? Explain.
- 20 -
Consumer Math 30S
Probability Unit
6.
In a class of 32 students, 18 students take an Art option, 10 other students take a Drama option',
and the rest of the students take a Choir option. One student is selected at random. Find the
following:
a)
the odds in favour of the selected student taking Drama
C
4.,
b)
the odds against the selected student taking Choir
c)
I E,
the odds in favour of the selected student either taking Art or Choir
Complete the following chart:
Probability
of an event
occurring
(expressed
as a
decimal)
Odds in
favour of
the event
occuring
8.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
it-
The probability of a soccer game in a particular league going into overtime is 0.125. Find the
following:
a)
the odds in favour of a game going into overtime
b)
the odds in favour of a game not going into overtime
c)
If the teams in the league play 100 games in a season, about how many games would you
expect to go into overtime?
2
- 21 -
Consumer Math 305
Probability Unit
9.
Steve wants to flip a coin. He tells you that the odds in favour of him getting a head is 1:1. Do you
agree? Why?
10.
The odds in favour of purchasing jeans with a defect are 3:997.
a)
What are the odds in favour of purchasing jeans without a defect?
b)
What is the probability of purchasing jeans without a defect?
- 22 -
Consumer Math 30S
Probability Unit
Lesson 5- Finding Expected Values Using Probability
When you complete this lesson, you will be able to
• complete an expected value chart
• determine the expected value of a simple game
Expected value is an application of probability which involves the likelihood of a gain or a loss. Expected
value is relevant in business, insurance, and many situations in your daily life.
The gain or loss associated with each event is known as its payout. In many games, you pay a given
amount to play. If you win the game, you receive a payout. But is the game worth playing?
In this lesson you will be introduced to the concept of expected value by looking at the expected value of
simple games. In the next lesson you will find the expected value in more involved situations.
The following example will demonstrate how you can determine the expected value of a simple game.
Activity
For this activity, you and your partner need 20 bingo chips (pennies, whatever) and a 6-sided die. You can
repeat this activity as many times as needed until a definite pattern emerges.
One person will act as the banker and will have 15 bingo chips. The other partner will have 5 bingo chips.
The partner must pay the banker 1 chip each time the game is played. If the partner rolls a 5 on the die, the
banker pays him or her 3 chips.
After a few rounds, switch roles. Are the results the same?
a)
What happened in each of the groups?
b)
Would you play this game with money? Why or why not?
c)
Does the player have much of an expectation of winning at this game? Why or why not?
The concept of expected value can be used to determine whether you should play games of chance.
Expected value is an estimate of the average return or loss you have when playing a game of chance.
Expected value can be found using the formula:
Expected value = (probability of winning)(gain)— (probability of losing)(loss)
- 23 -
Consumer Math 30S
Probability Unit
Example 1
Consider the following game. You have a 1 in 5 chance of winning the game and a 4 in 5 chance of losing.
The game costs $1 each time you play. If you win the game, you receive $4. If you lose the game, you
receive nothing. Find the expected value of the game.
Some students find it helpful to complete the following chart when finding expected value.
Event
Probability
Amount Won
Cost of
Playing
Payoff
Probability x
Payoff
Expected
Value
it
In general the following is true.
• If you play any game with an expected value <0, you can expect to lose money.
• If you play any game with an expected value = 0, you can expect to break even.
• If you play any game with an expected value >0, you can expect to gain money.
Every time you play the above game you can expect to
If you play the game
ten times, you can expect to
Example 2
Consider the following game. It costs $3 each time you play. You have a 1 in 10 chance of winning $25, a 1
in 5 chance of winning $5, and a 7 in 10 chance of receiving nothing.
a.
Find the expected value.
Event
Probability
Amount Won
Cost of
playing
Payoff
/
b.
If you play this game many times, will you gain or lose money?
- 24 -
Probability x
Payoff
Expected
Value
Consumer Math 30S
Probability Unit
Example 3
Consider the following game. It costs $1 each time you roll a six-sided number cube. If you roll an even
number you receive $2. If you roll an odd number, you receive nothing.
a.
Find the expected value of this game.
Event
Probability
,
Amount Won
.
'4)
-
Cost of
Playing
4r 1
(
1
b.
Payoff
:
i
4 ., t,
If you play this game many times, will you gain or lose money?
- 25 -
.
.
44._ i 4
.,› t,.,
“"--)ji
Lc
,
V-{ 6 (frtfr
Probability x
Payoff
kj-11
Expected
Value
t
‘-,i
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-
Consumer Math 30S
Probability Unit
Assignment 5— Finding Expected Values Using Probability
Consider the following game. It costs $2 each time you play. You have a 1 in 4 chance of winning
the game and a 3 in 4 chance of losing. If you win the game, you receive $10. If you lose the game,
you receive nothing. Complete the following chart and find the expected value of the game.
1.
Event
2.
Amount Won
f) c) it
_
,-,
Payoff
A
-‘ i
P
Probability x
Payoff
Expected
Value
1.
-3
•
( i
3
4
,
1eI:' ) g S t;
Consider the following game. It costs $2 each time you play. You have a 2 in 5 chance of winning
the game and a 3 in 5 chance of losing. If you win the game, you receive $4. If you lose the game,
you receive nothing. Complete the following chart and find the expected value of the game.
Event
Probability
Amount Won
d
2 )1
2,
1
3.
Cost of
Playing
12i
LA,{ ilil
i
Probability
"--
5
i.„
iC
Cost of
Playing
c," 2<4?
2._
Payoff
1
22
- 12_
Probability x
Payoff
c,fifc;
Expected
Value
Eil
ki
, „,...2-
Consider the following game. It costs $3 each time you play. You have a 1 in 10 chance of winning
$20, a 1 in 5 chance of winning $5, and a? in 10 chance of receiving nothing. Complete the
following chart and find the expected value of the game.
Event
Probability
Amount Won
Cost of
Playing
Payoff
i
'1
4
Probability x
Payoff
Expected
Value
,
if,
7
,
, I-
i ,; -5
I
I? 'I—)
'9
",)
4
,
- 26 -
— ,y
2-
t 14 i
i
Consumer Math 30S
Probability Unit
4.
Consider the following game. It costs $3 each time you roll a six-sided number cube. If you roll a 6
you win $15. If you roll any other number, you receive nothing.
a.
Complete the following chart and find the expected value of the game.
Event
b.
Probability
Amount Won
Cost of
_
- Playing
Payoff
Probability x
Payoff
Expected
Value
If you play this game many times, will you gain or lose money?
(
5.
Consider the following game. It costs $2 each time you draw a card from a shuffled deck. If you
draw a diamond you win $10. If you draw any other card, you receive nothing.
a.
Complete the following chart and find the expected value of the game.
Event
b.
Probability
Amount Won
Cost of
Playing
Payoff
If you play this game many times, will you gain or lose money?
- 27 -
Probability x
Payoff
Expected
Value
Consumer Math 30S
Probability Unit
6.
Consider the following game. It costs $1 each time you toss two coins. If both coins land tails you
win $3. If the coins land in any other way, you receive nothing.
a.
Complete the following chart and find the expected value of the game.
Event
Probability
Amount Won
Cost of
Playing
Payoff
Probability x
Payoff,,c
Expected
Value
Li
p
b.
If you play this game many times, will you gain or lose money?
7
Consider the following game. It costs $5 each time you draw a card from a shuffled deck. If you
draw an ace you win $50. If you draw any other card you receive nothing.
a.
Complete the following chart and find the expected value of the game.
Event
Probability
Amount Won
Cost of
Playing
*
I
b.
Payoff
If you play the game many times, will you gain or lose money?
- 28 -
Probability x
Payoff
Expected
Value
Consumer Math 30S
Probability Unit
Lesson 6 — Finding Expected Values Using Probability — Part 2
Expected value can also be used to determine whether or not it is a good idea to bid on a contract, grow a
certain crop, deliver flyers, etc.
Example 1
Based on past experience, a building contractor estimates that the probability of winning a contract is 0,30.
The contract is worth $25,000 and she knows it will cost her $2,400 to prepare a contract proposal.
a)
Find the expected value of the contract proposal.
the probability of winning is:
A
3
the amount of gain if she wins the contract is:
7_
the probability of losing is:
the amount of loss (cost to bid):
‘,2
EV = (prob. win)(gain)— (prob. loss)(loss)
b)
Is it financially a good idea for her to bid on the contract?
tje S
c)
c)
-
What other factors might she consider before making a decision?
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Consumer Math 30S
Probability Unit
I
Example 2
A farmer is deciding whether it is worthwhile to grow mixes •
crop in one of his fields. He knows from
experience that he will be able to harvest a crop 0 ears out of 10 Seeding, fertilizing, and harvesting cost
him $200 per acre. He estimates revenue from a good harvest to be $350 per acre.
Should he continue growing crops in this field? How much money will he make or lose if he is farming a
160-acre field?
probability of winning is:
the amount of gain is:
the probability of losing is:
the amount of loss is:
EV = (prob. win)(gain) — (prob. loss)(loss)
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Consumer Math 30S
Probability Unit
Assignment 6 — Finding Expected Values Using Probability — Part 2
1.
Based on past experience, a systems engineer sets the probability of winning a computer contract
at 0.25. The contract is worth $10,000 and the engineer calculated it would cost her $1,800 to
prepare a contract proposal.
a)
How much will the engineer gain if she wins the contract?
Kim
b)
How much will the engineer lose if she does not win the contract?
13( ktrJ
d)
Find the expected value of the contract proposal.
0.2 S
ZOO
X 0,25
e)
ovt
Is it financially a good idea for the engineer to bid on the contract?
c)
Name some other factors she might consider in deciding whether or not to bid on the contract.
2
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Consumer Math 30S
Probability Unit
2.
A carpet cleaning company-uses flyers to promote its business. The company knows that on
average 1 out of every 100 hiouseholds receiving its flyer will use its service. On average, the
company rneke-§—a—p-ITArbi$50.00 on each household whose carpets it cleans. It costs the
company $0.25 for each flyer.
a)
Find the expected value of each flyer.
,
(,)
C , 2S
b)
Find the expected value of 10,000 flyers.
/0,
c)
x
Is it financially a good idea for the company to send out flyers?
A manufacturer builds and sells birdbaths. He knows that, on average, 13 birdbaths per 100 are
defective. It costs him $12 to build each birdbath and he can sell them for $18 each. He plans on
building 100,000 this year. Will the manufacturer make or lose money on birdbaths this year?
r
0,
z
6
—
p
-2‘
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