Probability Practice
AP Statistics
Name:_____________________________
Date:__________ Period:_____________
I. Multiple Choice. For the following multiple choice questions, determine which answer best answers
the question. Then, explain why.
1. Suppose that the probabilities that an answer can be found on Google is 0.95, on Answers.com is 0.92, and
on both Web sites is 0.874. Are the possibilities of finding the answer on the two Web sites independent?
a) Yes, because (0.95)(0.92) = 0.874
b) No, because (0.95)(0.92) = 0.874
c) Yes, because 0.95 > 0.92 > 0.874
d) No, because 0.5(0.95 + 0.92) ≠ 0.874
e) There is insufficient information to answer this question.
Why?____________________________________________________________________________________
_________________________________________________________________________________________
2. There are five outcomes to an experiment and a student calculates the respective probabilities of the
outcomes to be 0.34, 0.50, 0.42, 0, and -0.26. The proper conclusion is that:
a) The sum of the individual probabilities is 1.
b) One of the outcomes will never occur.
c) One of the outcomes will occur 50 percent of the time.
d) All of the above are true.
e) The student made an error.
Why?____________________________________________________________________________________
_________________________________________________________________________________________
3. There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw
between 45 percent and 55 percent heads; in the second game, you win if you can throw more than 60 percent
heads. For each game, would you rather flip the coin 30 times or 300 times?
a) 30 times for each game
b) 300 times for each game
c) 30 times for the first game, and 300 for the second
d) 300 times for the first game, and 30 for the second
e) The outcomes of the games do not depend on the number of flips.
Why?____________________________________________________________________________________
_________________________________________________________________________________________
4. Suppose two events, E and F, have nonzero probabilities p and q, respectively. Which of the following is
impossible?
a) p + q > 1
b) p – q < 0
c) p / q > 1
d) E and F are neither independent nor mutually exclusive.
e) E and F are both independent and mutually exclusive.
Why?____________________________________________________________________________________
_________________________________________________________________________________________
II. Free Response
5. A random survey of 250 married individuals classified marital happiness versus income with the following
results:
Income
High
Average
Low
Unhappy
10
20
20
Happiness Level
Mildly Happy
Very Happy
25
30
55
45
25
20
(a) What is the probability that a person selected at random from this sample has an average income?
(b) What is the probability that a person selected at random from this sample has low income and is very
happy?
(c) What is the probability that a person selected at random from this sample is mildly happy with their
marriage?
(d) Is being mildly happy with your marriage and having an average income independent of each other? Why
or why not?
6. Imagine you shuffle a standard deck of 52 cards and draw a card at random.
Event A = {drawing a spade}
Event B = {drawing an 8}
Event C = {drawing a 5}
Event D = {drawing a card less than 4} (ace included)
Find the probability of the following:
(a) P(A)
(d) P(D)
(b) P(B)
(e) P(C)
(c) P(A ∩ B)
(f) P(C ∪ D)
(d) P(Ac)
(h) P(Ac ∩ C)