Nov. 13, 2000
(1) Suppose that A and B are subsets of a universal set U, and that n( U ) = 50, n(A) = 10, n(A ∪ B) = 20, and n(A ∩ B) = 3. Supply the following information.
(a) n( A' ) =
(b) n( B ) =
(c) n( A' ∪ B ) =
(d) n( A' ∩ B ) =
(a) In how many ways can you choose a committee of 4 people from a group of 10 people?
(b) From a group of 10 people, you select a president, a vice-president, a
secretary and a treasurer. In how many ways is this possible?
(3) Suppose A and B are events, and P(A) = 1/2, P(B) = 1/3, and P(A
∪ B) = 2/3.
Are A and B independent, dependent, or is there not enough information given to say for sure? Explain.
(4) One card is drawn off a 52-card deck. What is the probability that
(a) a heart or a King?
(b) a heart and a King?
(c) neither a heart nor a King?
(d) a heart, given that it's also a King?
(5) A coin is tossed 6 times. What is the probability that ...
(a) the first 2 tosses are heads?
(b) exactly 2 of the 6 tosses are heads?
(c) less than 2 of the 6 tosses are heads?
(d) the first 2 tosses are heads or the last toss is a head?
(6) At a certain college, 40% of the students are male, and 60% are female. Also, 20% of the males are smokers, and 10% of the females are smokers.
(a) A student is chosen at random. What is the probability that the student is a male nonsmoker?
(b) A student is chosen at random. If the student is a smoker, what is the probability that the student is female?