Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
PROBABILITY
Probabilities Through Simulation
Solve the problem.
1) A firm uses trend projection and seasonal factors to simulate sales for a given time period.
It assigns ʺ0ʺ if sales fall, ʺ1ʺ if sales are steady, ʺ2ʺ if sales rise moderately, and ʺ3ʺ if sales
rise a lot. The simulator generates the following output.
1)
0 1 0 2 2 0 0 1 2 3 2 0 2 0 2 2 1 2 3 1 2 2 2 0 3 0 0 2 1 2 1
Estimate the probability that sales will remain steady.
Use a graphing calculator to develop a simulation of the given problem (100 trials). Describe the simulation, then
estimate the probability based on its results.
2) The probability of getting exactly three girls in a family of five children.
2)
Press MATH
select PRB
choose randInt
enter the minimum 0, the maximum 1 and 5 for the number of values.
press ENTER
repeat the stepts 6 times.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
3) The probability of getting at least two boys in a family of seven children.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
3)
Answer Key
Testname: 16_PROBABILITIES_6 SIMULATION
1) 0.194
2) Answers may vary. Begin by representing girls as odd numbers and boys as even numbers. Then use a calculator or
computer program to generate 5 random integers. Count as a success if exactly 3 of the numbers generated are odd.
Repeat for 100 trials. The estimated probability is the number of successes divided by 100. Estimated probability is
about 0.31.
3) Answers may vary. Begin by representing girls as odd numbers and boys as even numbers. Then use a calculator or
computer program to generate 7 random integers. Count as a success if 2 or more of the numbers generated are even.
Repeat for 100 trials. The estimated probability is the number of successes divided by 100. Estimated probability is
about 0.94.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
PROBABILITY
The Addition Rule
Determine whether the events are mutually exclusive.
1) Draw one ball colored red from a bag.
Draw one ball colored blue from the same bag.
2) Meet a man with an umbrella.
Meet a man with a raincoat.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
1)
2)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Find the indicated probability.
10
3) If P(A) = , find P(A).
11
3)
4) Find P(A), given that P(A) = 0.662.
4)
5) Based on meteorological records, the probability that it will snow in a certain town on
January 1st is 0.206. Find the probability that in a given year it will not snow on January
1st in that town.
5)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
6) If a person is randomly selected, find the probability that his or her birthday is not in May.
Ignore leap years.
6)
7) A spinner has equal regions numbered 1 through 15. What is the probability that the
spinner will stop on an even number or a multiple of 3?
7)
8) If you pick a card at random from a well shuffled deck, what is the probability that you
get a face card or a spade?
8)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
9) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
433
42
71
37
583
Women
326
47
78
39
490
Total
759
89
149
76
1073
If one of the 1073 people is randomly selected, find the probability that the person is a man
or a heavy smoker.
9)
M = the person is a man;
HS = the person selected is a heavy smoker.
We need to find:
P(M or HS) = P(M)+P(HS)-P(M and HS).
From the table we find 1073 people in total; 583 men; 76 heavy smokers and also we can find
37 who are men and heavy smokers on the same time.
So, P(M or HS) = 583/1073 + 76/1073 - 37/1073 = 622/1073 = 0.58.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
10) 100 employees of a company are asked how they get to work and whether they work full
time or part time. The figure below shows the results. If one of the 100 employees is
randomly selected, find the probability of getting someone who carpools or someone who
works full time.
10)
1. Public transportation: 9 full time, 6 part time
2. Bicycle: 4 full time, 5 part time
3. Drive alone: 31 full time, 30 part time
4. Carpool: 7 full time, 8 part time
C = someone who carpools
FT = someone who works full time.
P(C or FT) = P(C) + P(FT) - P(C and FT) = 15/100 + 51/100 - 7/100 = 59/100 = 0.59.
(We found 51 full-time workers adding up the corresponding numbers per categories; 7 of them are also
carpooling)
11) A 6-sided die is rolled. Find P(3 or 5).
11)
P(3 or 5) = P(3) + P(5) - P(3 and 5) = 1/6 + 1/6 - 0 = 2/6 = 1/3.
P(3 and 5) = 0 because the events (getting a 3" and the event "getting a 5" are mutually exclusive.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
12) A card is drawn from a well-shuffled deck of 52 cards. Find P(drawing an ace or a 9).
12)
Getting an ace and getting a 9 are mutually exclusive, so that P(A and 9) = 0.
P(A or 9) = P(A) + P(9)= 4/52 + 4/52 = 8/52 = 2/13.
13) The table below describes the smoking habits of a group of asthma sufferers.
Occasional Regular Heavy
Nonsmoker
smoker
smoker smoker Total
Men
370
45
61
39
515
Women
443
39
84
38
604
Total
813
84
145
77
1119
If one of the 1119 people is randomly selected, find the probability of getting a regular or
heavy smoker.
R = regular smoker
HS = heavy smoker
P(R or HS) = P(R) + P(HS) - P(R and HS) = 145/1119 + 77/1119 - 0 = 222/1119 = 0.198.
R and HS are mutually exclusive.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
13)
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
14) 100 employees of a company are asked how they get to work and whether they work full
time or part time. The figure below shows the results. If one of the 100 employees is
randomly selected, find the probability that the person drives alone or cycles to work.
14)
1. Public transportation: 10 full time, 9 part time
2. Bicycle: 3 full time, 4 part time
3. Drive alone: 28 full time, 29 part time
4. Carpool: 9 full time, 8 part time
Similar with Exercise 10.
15) A bag contains 7 red marbles, 4 blue marbles, and 1 green marble. Find P(not blue).
P(not blue) = 1 - P(blue) = 1 - 4/12 = 2/3.
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley
15)
Answer Key
Testname: 13_ PROBABILITIES_3 ADDRULE
1) Yes
2) No
1
3)
11
4) 0.338
5) 0.794
334
6)
365
7)
2
3
8)
11
26
9) 0.580
10) 0.59
1
11)
3
12)
2
13
13) 0.198
14) 0.64
2
15)
3
Elementary Statistics, by M.F. Triola, 10th Ed., Addison Wesley