AP Statistics
Chapter 6 Probability Review
1. Define Probability.
2. List the four rules of probability:
Name:________________________________
3. What is the rule to test for independence? a.
If P(A) = 0.25 and P(B) = 0.34, what is P(A ∪ B) if A and B are independent?
4. What is the conditional probability rule? a. Suppose P(A) = 0.25 and P(B) = 0.40. If P(A|B) = 0.20, what is P(B|A)?
5. Describe the sample space of the following.
(a) Choose a student in your class at random. Ask how much time that student spent studying during the past 24 hours.
(b) In a test of a new package design, you drop a carton of a dozen eggs from a height of 1 foot and count the number of broken eggs.
(c) Tossing a coin and rolling a die simultaneously.

6. Police report that 78% of drivers stopped on suspicion of drunk driving are given a breath test, 36% a blood test, and 22% both tests.
(a) Using the General Addition Rule, find the probability that a randomly selected DWI suspect is given a blood test or a breath test.
(b) Represent this situation in a two-way table.
(c) Find the probability that a randomly selected DWI suspect is given:
1. P(either test) 2. P(only a blood test) 3. P(only a breath test) 4. P(neither test)
(d) Are the tests independent? Use probability rules to support your answer.
7. Suppose you have a standard deck of 52 cards. Find the probability of drawing a certain card given the following events:
A = {draw a diamond} B = {draw a black card} C = {draw a 4}
(a) P(A)
(f) P(A C ∩ B)
(b) P(B)
(g) P(B C )
(c) P(C)
(h) P(B C ∪ C)
(d) P(A C )
(i) P(C | B)
(e) P(A ∪ B)
(j) P(B | C)

8.
A recent survey of teenagers (12 – 17) found the following statistics:
57% of teenagers have a Facebook account
50% of teenagers have a Twitter account
37% of teenagers have a YouTube account
Further investigation showed that:
22% of teenagers have both a Facebook and Twitter account
6% have all three
13% of teenagers have both a YouTube and Facebook account
11% of teenagers only have a YouTube account
(a) Construct a Venn Diagram to represent this information.
(b) P(a teenager has none of the three)
(c) P(a teenager has only a Twitter account)
(d) P(a teenager has a YouTube account, given that they have a Facebook)
(e) P(a teenager has a Twitter and a YouTube account)
9. The probability that Travis makes a free throw is 0.6. Each shot is independent of the others.
(a) What is the probability that Travis makes three free throws in a row?
(b) What is the probability that Travis misses one free throw?
(c) Travis’ coach has asked him to shoot 10 free throws before the end of practice. What is the probability that Travis will make all 10 free throws? What is the probability that he will miss all 10 free throws?

10.
A travel agent books passages on three different tours, with half her customers choosing tour one (T
1
), onethird choosing tour two (T
2
), and the rest choosing tour three (T
3
). The agent noted that three-quarters of those who take tour one return to book passage again, two-thirds of those who take tour two return, and one-half of those who take tour three return. If a customer does return, what is the probability that the person first went on tour two? (Use a tree diagram.)
11. (6.79) All human blood can be “ABO-typed” as one of O, A, B, or AB, but the distribution of the types varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in the United States:
Blood Type:
U.S. probability:
O
0.45
A
0.40
B
0.11
AB
?
(a) What is the probability of type AB blood in the United States? Why?
(b) An individual with type B blood can safely receive transfusions only from persons with type B or type O blood. What is the probability that the husband of a woman with type B blood is an acceptable blood donor for her?
(c) What is the probability that in a randomly chosen couple the wife has type B blood and the husband has type A?
12.
Three cards are to be selected from a deck of cards without replacement.
(a) What is the probability that the first card selected is a jack?
(b) Given the first card is a jack, what is the probability of the second card being a 5?
(c) Given the first card is a jack and the second card is a 5, what is the probability of the third card being an ace?
(d) What is the probability of selecting a jack, then a 5, then an ace?