Unit 4.1
Unit 4.2
Unit 4.3
100
Which of the following statements is false?
(a) All possible outcomes together must have probabilities that add up to 1.
(b) A phenomenon is random if individual outcomes are uncertain.
(c) The probability of any outcome must be a number between 0 and 1.
(d) A probability can be a number greater than 1.
(D) A Probability can be a number greater than 1.
100
If P(A) = .24 and P(B) = .52 and A and B are mutually exclusive, what is P(A or B)?
(a) .1248
(b) .28
(c) .6352
(d) .76
(D) .76
100
There are 10 applicants applying for three positions: hostess, server and busser. How many
ways can these three positions can be filled by the 10 applicants?
Ans: 720 ways
200
During his NBA career, Larry Bird made approximately 89% of all free throws. Suppose Larry
makes 10 free throws in a row. Assuming each free throw is independent, what is the probability
he will make the next free throw?
(a) 0.11
(b) 0.50
(c) 0.01
(d) 0.89
(D) 0.89
200
Suppose 70% of all adults drink coffee. If you were to conduct a simulation involving coffee-
drinkers and non-coffee drinkers, which of the following is a valid assignment of digits to
represent coffee drinkers?
(a) 0, 1, 2 = coffee drinker; 3, 4, 5, 6, 7, 8, 9 = not a coffee drinker.
(b) 0, 1, 2, 3 = coffee drinker; 4, 5, 6, 7, 8, 9 = not a coffee drinker.
(c) 0, 1, 2, 3, 4 = coffee drinker; 5, 6, 7, 8, 9 = not a coffee drinker.
(d) 0, 1, 2, 3, 4, 5, 6 = coffee drinker; 7, 8, 9 = not a coffee drinker.
(D) 0, 1, 2, 3, 4, 5, 6 = coffee drinker; 7, 8, 9 = not a coffee drinker.
200
In a recent poll, 13% of all respondents said that they were afraid of heights. Suppose this
percentage is true for all Americans. Assume responses from different individuals are
independent.
(a) What is the probability of having 3 randomly selected Americans all say that they are afraid
of heights?
(b) What is the probability of having none of the 3 randomly selected Americans say that they
are afraid of heights?
(c) What is the probability of having at least 1 of the 3 randomly selected Americans say that
they are afraid of heights?
Ans:
(a) P(3 people afraid of heights) = (0.13)3 = 0.002
(b) P(3 people not afraid of heights) = (1 – 0.13)3
= 0.659
(c) P(At least 1 person afraid of heights) = 1 – 0.659 = 0.341
300
A statistics teacher states the probability of a surprise quiz on any given day is 0.30. If
quizzes are given independently each day, what is the probability there will be a surprise quiz
on the next two consecutive days?
(a) 0.09
(b) 0.21
(c) 0.42
(d) 0.60
(A) 0.09
300
Consider the following probability model associated with the type of sneakers worn by high
school basketball players in Massachusetts. What is the probability a randomly selected
Massachusetts high school basketball player wears Adidas or Reebok sneakers?
(a) 0.065
(b) 0.580
(c) 0.420
(d) 0.225
(c) 0.420
300
A local restaurant is handing out coupons to customers as part of a marketing promotion.
The coupons are all of equal size, well mixed, and have the name of a free item written on them.
Here is the probability model for the items the customers can win:
(b) Find the probability that a customer won’t win an entree.
(a) The probabilities add up to 1 and each probability is between 0 and 1.
(b) P(Won’t win an entrée) = 0.95
400
Two events are said to be mutually exclusive if:
(a) they both contain the same outcomes.
(b) they do not contain any outcomes in common.
(c) they both have at least one outcome in common.
(d) one event contains all of the outcomes that are not contained in the other event.
(B) they do not contain any outcome in common.
400
You play tennis regularly with a friend, and from past experience, you believe that the
outcome of each match is independent. For any given match you have a probability of 0.6 of
winning. The probability that you lose the next two matches is
(a) 0.16
(b) 0.40
(c) 0.64
(d) 0.36
(A) 0.16
400
A soccer team has 12 players on the field at the end of a scoreless game. According to
league rules, the coach must select 5 of the players and designate an order in which they will
take penalty kicks.
(a) Is this a permutation or a combination? Why?
(b) How many different ways are there for the coach to do this?
(a) Permutation, the coach has to pick the players and the order they kick so the order
matters.
(b) 12C5 = 95,040 ways
500
The probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10,000. Each
play of the lottery is independent of the next play.
(a) Explain what this probability means.
(b) If 10000 people play the Pick 4 lottery, will exactly 1 person win the lottery? Explain.
(c) The winning number in a Pick 4 lottery was 1234 two days in a row. What is the likelihood of
this number occurring on the next drawing? Explain.
(a) If you take a very large random sample of purchased lottery tickets, about 0.01% of the
tickets will be winners.
(b) No. Probability describes what happens in many, many repetitions of a chance process.
We would expect to get about 1 winning ticket out of 10000 tickets, but this result is not
guaranteed.
(c) Even after the winning number was 1234 two days in a row, the probability that 1234 is the
winning number is still the same 1/10,000. The probability does not change.
500
Suppose you spin a spinner with four equal sections (red, blue, green and yellow) two times.
(a) List out all of the possible outcomes for spinning two times.
(b) Define event A as spinning blue at least once. Find P(A).
500
Among 120 middle school students, 70 like chocolate ice cream, 40 like strawberry ice
cream, and 30 like both. A middle school student is randomly selected.
(a) Make a Venn diagram to display the sample space of this chance process using the events
C: likes chocolate ice cream and S: likes strawberry ice cream.
(b) Find the probability that a randomly selected middle school student like chocolate or
strawberry ice cream.
(c) Find the probability that a middle school student likes chocolate ice cream and not
strawberry ice cream.
(d) What’s the probability that a randomly selected middle school student likes chocolate ice
cream, given that they like strawberry ice cream?
