Assignment 1

p2.

• 1.  In a classical card game, we get 5 cards from a deck • of 52. Find the probabilities of:• (a)   1-pair• (b)   2-pair• (c)   3-of-a-kind • (d)   full house• (e)   4-of-a-kind• (f)   a straight• (g)   a flush (but not flush straight)• (h)   a flush straight• (i)    nothing

p3.

• 2. In a bridge game, North and South have total 7 cards• of spades (out of 13 spade cards). Find the probabilities• of (x, y)’s in the following questions where West holds • x cards of spades and East y cards of spades?

• (a)Pr((x,y) is (0, 6) or (6, 0))• (b)Pr((x,y) is (1, 5) or (5, 1))• (c)Pr((x,y) is (2, 4) or (4, 2))• (d)Pr((x,y) is (3, 3))

p4.

• 3. From a faculty of six professors, six associate professors, ten assistant professors, and twelve instructors, a committee of size six is formed randomly. What is the probability that there is at least one person from each rank on the committee?

(See hint at #21, p.73 in the text.)

p5.

• 4. A four-digit number is selected at random. What is the probability that its ones place is greater than its tens place, its tens place is greater than its hundreds place, and its hundreds place is greater than its thousands place? Note that the first digit of an n-digit number is nonzero.