SOLUTION: If you roll a pair of dice five times, find the probability of each outcome. -You get doubles exactly once. -You get exactly three sums of 7. -You get at least one sum of 7

Question 1160749: If you roll a pair of dice five times, find the probability of each outcome.
-You get doubles exactly once.
-You get exactly three sums of 7.
-You get at least one sum of 7.
-You get at most one sum of 7.
Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
.

            There are two totally different problems in this post.

            Therefore, I will answer (b), (c) and (d) ONLY   (since these three parts logically comprise one problem)

The probability to get the sum of 7 at each single roll a pair of dice is  

     ( since there are 36 outcomes, in total, and only six are successful, 

     (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1) ).


So the answers (and the solutions) are



(b)  P =  = 0.03215.


(c)  P = 1 -  = 0.598122.


(d)  P =  +  = 0.803755.

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