HW #2 Due 1/27/04 Stat 310 D.Scott
1. List all possible events associated with a single toss of a tetrahedral die (4-sided).
In particular, think about a sensible way to record the result of a single toss of a
tetrahedral die.
2. Prove P(A∪B)≤P(A) + P(B).
3. What is P(A∪B∪C) in terms of known probabilities of events A,B,C,A∩B,A∩C,
B∩C,A∩B∩C?
4. For 5-card poker hands, find (a) ν(3 of a kind); (b) ν(full house); (c) ν(1 pair); (d)
ν(Ace high). Note: ν(·)denotes the “number of ways.”
5. From 7 men and 4 women, how many committees can be formed with (a) 3 men and
2 women; (b) 5 members, with at least 3 men?
6. What is the probability that if npeople are present in the same room, at least two
will have the same birthday? Plot your answer for nless than 40.
Note: Please fold your homework in half lengthwise, staple pages together, and print your
name on both the inside and outside.
Poker Hands (in order)
1. Royal Flush (AKQJ10, one suit)
2. Other straight flushes (45678, one suit, Ace low OK)
3. Four of a kind (KKKK8)
4. Full house (AAA22, three-of-a-kind plus one pair)
5. Flush (5 cards same suit, not in sequence)
6. Straight (23456 different suits, Ace low OK)
7. 3 of a kind (555JK)
8. Two pair (AAQQ7)
9. Pair (AA268)
10. “Nothing” (Queen high, for example)
Order of suits (best to worst): Spades, Hearts, Diamonds, Clubs.
Course webpage: http://www.stat.rice.edu/∼scottdw/stat310/