These are your guided notes for the entire Unit please keep up with them.
What is Probability?

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a
number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher
the probability of an event, the more certain we are that the event will occur.

𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑎𝑛 𝑒𝑣𝑒𝑛𝑡 ℎ𝑎𝑝𝑝𝑒𝑛𝑖𝑛𝑔 =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑖𝑡 𝑐𝑎𝑛 ℎ𝑎𝑝𝑝𝑒𝑛
Total number of outcomes
How do we use probability?

Probabilities: We talk about the probability/chance of getting a certain result everyday. E.g., we
say, "There is 90% chance (probability) that there will be rain today." When we make bets, we
also estimate probabilities: "There is a 50/50 chance of getting a head or tail on the next coin
toss."
How do we write probabilities?

As a percentage fraction or proportion.
What is a Venn Diagram?

a diagram that shows all possible logical relations between a finite collection of different sets.
Typically overlapping shapes, usually circles, are used, and an area-proportional or scaled Venn
diagram is one in which the area of the shape is proportional to the number of elements it
contains
How do we use Venn Diagrams?


Venn diagrams are used to compare and contrast groups of things.
A Venn diagram consists of overlapping circles. Each circle contains all the elements of a set.
Where the circles overlap shows the elements that the set have in common. Generally there are
two or three circles.
Why do we use Venn Diagrams?

Venn diagrams are widely used as a tool for thinking. They are therefore also
a useful teaching strategy.

They can be useful for practising making logic statements, e.g., if/then,
all/some/no, may be.

Ex 1. Ms. Snow conducted a survey of her homeroom. She asked students what math course
and what science course they were taking this semester. Below are the results.
a. Which part shows only the students who are taking only Algebra 2? Only Chemistry? Both
Chemistry and Algebra 2? Neither Chemistry nor Algebra 2?
b. What does it mean to select a probability of an event with 2 characteristics?
c. What does it mean to select a student who is taking algebra 2 or chemistry?
d. If a student is selected at random from Ms. Snow’s homeroom, what is the probability that the
student is taking Algebra II and Chemistry? Explain your reasoning.
e. If a student is selected at random from Ms. Snow’s homeroom, what is the probability that the
student is not taking Algebra II or Chemistry? Explain your reasoning.
f.
Find the probability of a student taking Chemistry, given that the student is not taking Algebra II,
or P(Chemistry/not taking Algebra II).
Ex 2. Students survey 758 spectators at a national championship tennis match. The survey results
indicate the following:
• 421 are male,
• 256 have a two-handed backhand swing,
• 176 of the people with a two-handed backhand swing are female.
a. Draw a Venn Diagram.
b. What is the probability that a person selected at random from the survey group is male? Explain
your reasoning.
c. What is the probability that a person selected at random from the survey group is female?
Explain your reasoning.
d. What is the probability that a person selected randomly from the survey group has a twohanded backhand swing? Explain your reasoning.
e. What is the probability that a person selected randomly from the survey group is a male or has a
two-handed backhand swing? Explain your reasoning.
f.
What is the probability that a person selected randomly from the survey group does not have a
two-handed backhand swing, given that the person is male, or P(no two-handed
backhand/male).
QUIZ
TREE DIAGRAMS
What does the term equally likely mean?
What is a tree Diagram?
Make a tree diagram to show the group the possible paths customers might take, entering the maze on
the upper, middle, or lower path and proceeding to an exit with or without a pumpkin.
a. What is the probability you will select a sandwich with white bread? Explain your reasoning.
b.
What is the probability you will select a sandwich with American cheese? Explain your
reasoning
c. What is the probability that you will select a sandwich on wheat bread with ham and any
cheese? Explain your reasoning.
d. What is the probability you will select a sandwich on white bread that has either beef or turkey
and has Provolone cheese? Explain your reasoning.
e. What is the probability you will select a sandwich with neither beef nor Muenster cheese?
Explain your reasoning
Draw a tree diagram to show all the possible combinations of volunteers who might go with Catrina.
How many outcomes are in the sample space?
Are all the outcomes equally likely? What would make the outcomes not equally likely?
What is the probability that Nathan will be selected? Explain your reasoning. List the possible outcomes
for 2-person committees that include Nathan.
MAJOR ASSESSMENT: GROUP/PAIR PROJECT GAME DAY…
WORK ON PROJECT
PLAY THE GAMES
TEST
Expected Value Notes and Example Problems
What is Expected Value?
When is expected value used?
How do you find expected value?
Examples:
1.) In a game, you are to roll a dice. If you roll an odd number, you win $2. If you roll an even
number, you lose $3. What is the expected value of the game?
2.) You ask your parents for money. Being math minded people who want you to think, they each
give you a mathematical answer. Your mom says for money you must flip a coin, if it is heads
you get $10 and if it is tails, you get $5. Your dad on the other hand, says if you get heads, he
will give you $30, but if you get tails you must pay him $20. Which should you choose?
3.) A raffle has a grand prize of $10,000. It also has 3 lower prizes of $100 each. There are 20,000
tickets sold for $5 each. What is your expected value.
4.) At a particular game, you are to draw a card from a regular deck of cards (with no jokers). If it is
a heart, you win $10. If it is a face card of another suit, you win $8. Any other card, you lose $6.
Should you play? Why?
5.) A grab bag at a children’s store has packages of toys in it. It has 12 toys worth 80 cents, 15 worth
40 cents, and 25 worth 30 cents. Is it worthwhile to buy a grab bag if it cost 50 cents to pick at
random?
6.) At another game, you are to roll a dice twice. If the sum is 2 – 6, you win $10. If the sum is
higher than 6, you lose $5. Should you play?
7.) You pay $10 to play a game where you reach in a bag and grab one bill that you get to keep. In
the bag there is 1 $100 bil, 3 $20 bills, 2 $50 bills, 3 $10 bills, 8 $5 bills, and 28 $1 bills.
a. How much should you expect to win or lose?
b. After 100 people play the game, how much should the game owners expect to make?
8.) At a horse race, Soon-To-Be-Glue is running. It cost $1000 to bet on him. If he gets first place (a
1/20 chance), you win $4,500. If he gets 2nd place (a 1/10 chance), you win $3500. If he gets 3rd
place (a ¼ chance), you win $1500. Is it worth it to bet?
9.) In a game, you flip a coin twice and record the number of tails that occur. You get 10 points for 2
tails, 0 points for 1 tail, and 5 pints for no tails.
a. How many points can you expect to get?
b. If you played 50 times, how many points do you think that you would have?
10.) In a pick 3 game, there are 3 bins with 10 balls each having a digit between 0 and 9 printed on it.
It cost $1 to play. You win $500 if you guess exactly the numbers you pick (in the same order).
How much money would you end up with if you played every day for a year?
11.) Your new TV comes with a 1 year warranty. Best Buy sells an extended warranty for $50. If you
buy the contract, all repairs for an additional 3 years are free. Consumer Reports shows a 10%
chance of TV’s like the one you bought require a repair costing on average $150 in the 2nd, 3rd, or
4th year of ownership. Should you buy the warranty?
12.) At another game, you are to reach into a bag that has 7 red blocks and 3 blue blocks. Then you
pick out of another bag with 2 red blocks and 8 yellow blocks. If you do not pick red, you win $8.
If you get 2 reds, you win $15. You must pay $4 to play. What is your expected value?
16.)
Jennifer is playing a game at an amusement park. There is a 0.1 probability that
she will score 10 points, a 0.2 probability that she will score 20 points, and a 0.7 probability
that she will score 30 points. How many points can Jennifer expect to receive by playing the
game?
16.)
Linda estimates the number of questions she answered correctly on a test. She
answered 10 correctly with probability 0.6, 20 correctly with probability 0.3, and 50 correctly
with probability 0.1. What is the expected value of the number of questions Linda answered
correctly?
15.) A caterer has just prepared numerous specialty dishes to be sold. There is a 5/11 chance
that they will be sold today, in which case the profit will be $76. There is a 6/11 chance that they
will not be sold today, in which case the caterer will lose $31 since the caterer does not have
refrigerator space to store the dishes. Find the caterer’s mathematical expectation.
A card is drawn at random from an ordinary deck of cards. If the card selected is a face card, then
Trudy wins $15. If the card selected is an ace, then Trudy wins $20. Otherwise, she loses $10. What is her
mathematical expectation?
16.)
TEST
18.) There are twenty evenly sized spots on a spinner at a local carnival. Ten of the spots say $1,
5 of the spots say $2, 3 of the spots say $3, one says $5, and one says $10. If you spin the wheel
and win the amount of money shown, then how much money can you expect to win per spin if
you pay $4?