Homework 1 Due Friday, Jan. 22
1. The following table displays the 100 senators of the 112 th U.S. Congress on January 5, 2011, viewed by political party affiliation
and gender.
Male
Female
Total
Democrat
39
12
51
Republican
42
5
47
Independent
2
0
2
Total
83
17
100
A senator is selected at random from this group.
a) What is the probability that the senator is female?
b) What is the probability that the senator is a Republican and is male?
c) What is the probability that the senator is a Democrat or is female?
2. The game of craps is played with two dice. A player throws both dice, winning unconditionally if he produces a natural (the sum of
the numbers showing on the two dice is 7 or 11), and losing unconditionally if he throws craps (the sum is 2,3, or 12). Consider the
following events:
A: {Player throws craps}
B: {Player throws a natural}
C: {Sum of the two dice is 9, 10, or 11}
a) Which pairs of events, if any, are mutually exclusive? Why?
b) Which pairs of events, if any, are independent? Why?
3. In a certain county, 45% of the registered voters are Democrats, 35% are Republicans, and 20% are Independents. Sixty percent of
the Democrats, 80% of the Republicans, and 30% of the Independents favored increased spending to combat terrorism. If a person
chosen at random from the county does not favor increased spending to combat terrorism, what is the probability that the person is a
Democrat?
4. An experiment consists of flipping a fair coin once and rolling a fair die once. What is the probability of observing a head or a six?
5. Suppose that 70% of the orders on a particular website are shipped to the person who is making the order and the remaining 30%
are shipped to people other than the person placing the order. Gift wrapping is requested for 60% of the orders being shipped to other
people, but for only 10% of orders shipped to the person making the order.
a) What is the probability that a randomly selected order will be gift wrapped and sent to another person?
b) What is the probability that a randomly selected order will be gift wrapped?
c) Is gift wrapping independent of the destination of the gift? Justify your response statistically.
6. 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. A survey of the male students at a junior college reveals that, 21% play soccer regularly, 22% are Latino, and half of the Latino
students play soccer regularly. If a male student is selected at random, what is the probability that he is not Latino and does not play
soccer regularly?
8. A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time if the person
has the virus and 5% of the time if the person does not have the virus. If a person tests positive, what is the probability that the person
is infected?
9. The probability that a married man will vote in a specific election is 0.50, the probability that a married woman will vote in the
election is 0.60, and the probability that a married woman will vote in the election given her husband votes is 0.90.
a) What is the probability that a husband and wife both vote in the election?
b) What is the probability that a husband will vote, given that his wife votes?
c) What is the probability that at least one member of a married couple will vote?
10. For a four-question multiple-choice pop quiz, a student is totally unprepared and randomly guesses the answer to each question. If
each question has five options, then the probability of selecting the correct answer for any given question is 1/5, or .2. With guessing,
the response on one question is not influenced by the response on another question. Thus, whether one question is answered correctly
is independent of whether or not another question is answered correctly. Find the probability the student passes, answering at least
three questions correctly.