Exercise 1. Suppose that A and B are pairwise disjoint events for which P(A) = 0.3 and P(B) = 0.5.
- What is the probability that B occurs but A does not?
- What is the probability that neither A nor B occurs?
Exercise 2. Forty percent of the students at a certain college are members neither of an academic club nor a Greek organization. Fifty percent are members of an academic club and thirty percent are members of a Greek organization. What is the probability that a randomly chosen student is
- member of an academic club or a Greek organization?
- member of an academic club and of a Greek organization?
Exercise 3. In a seminar attended by 24 students, what is the probability that at least two of them have the same birthday ?
Honors Exercise: Find the probability of randomly drawing the following poker hands.
- A one pair, which consists of two cards of the same rank and three other distinct ranks. (e.g. 22Q59)
- A two pair, which consists of two cards of the same rank, two cards of another rank, and another card of yet another rank. (e.g.JJ779)
- A three of a kind, which consists of a three cards of the same rank, and two others of distinct rank (e.g. 4449K).
- A flush, which consists of all ve cards of the same suit (e.g. HHHH, SSSS, DDDD, or CCCC).
- (E) A full house, which consists of a two pair and a three of a kind (e.g. 88844). (Hint: Note that 88844 is a dierent hand than a 44488.)
Research and Lecture notes 