5. [40 pts.] In a game much simpler than Yahtzee sold by Hasbro, a player throws

Question

5. [40 pts.] In a game much simpler than Yahtzee sold by Hasbro, a player throws three ordinary six sided dice and tries to obtain various combinations of poker-like hands. In a throw of three dice compute the following: a) All three dice showing the same number. b) Two dice showing one number and the other die showing a different number. c) Three different numbers on the three dice. d) If the above computations (parts a, b, and c) account for all possible cases, the sum should be one. Are these all the cases and do parts a, b, and c sum to one or not?

Explanation / Answer

5. Total number of outcomes = 6^3 = 216

a. number of cases favourable to all 3 dice are showing same number = 6

required probability = 6/216 = 1/36

mean = 3

variance:

2=x2p(x)2

x2p(x)= 54/5

2=x2p(x)2=54/532=9/5= 1.8

k prob k*prob 1 0.2 0.2 2 0.1 0.2 3 0.4 1.2 4 0.1 0.4 5 0.2 1 Total 3

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