CEE 202 HW1 Solutions

# Sample space results of 5 die rolls n 6x6x6x6x6 65

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Unformatted text preview: ities. none2 = 3 x 25 = 75 Two “2”: Atwo2 = {22 ­, 2 ­2,  ­22} 3 possibilities The remaining one blank can be filled in 5 ways. ntwo2 = 3 x 5 = 15 Three “2”: Athree2 = {222} 1 possibility and only 1 way to do this nthree1 = 1 P = (75 + 15 + 1)/216 = 0.421 6. (25 points) In a game of Yahtzee, where 5 dice are tossed simultaneously, find the probability of getting: a) Three of a kind b) A full house (two of one kind and three of another kind) This is a challenging problem. Sample space: results of 5 die rolls N = 6x6x6x6x6 = 65 = 7776 a) Three of a kind Let’s start with the event “A = three 1s”. If you can get this right, the rest will be easier. One way to get the number of three ­1 events is to enumerate all the possible die rolls, where “x” is “any number but 1”. 111xx, 11x1x, 11xx1, 1x11x, 1x1x1, 1xx11, x111x, x11x1, x1x11, xx111 There are 10 possibilities. Another way to get this value is to label each die: A,B,C,D,E Now we select three of the dice to roll a “1”. How many possible combinations are there? "5% 5! n 3 of 5 = \$ ' = = 10 # 3& 3!2! In how many ways can the ‘x’ be filled in? They could each be 2,3,4,5,6 5x5 = 25, so there are 25 possible pairs ! 2/4 CEE 202 – Engineering Risk & Unce...
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## This document was uploaded on 03/06/2014 for the course CEE 202 at University of Illinois, Urbana Champaign.

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