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When three standard dice are tossed, the numbers a,b,c are obtained. Find the probability that (a-1)(b-1)(c-1)  not equal to 0

 May 19, 2020
 #1
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the only possible way (a-1)(b-1)(c-1) is not zero is if none of the dice have "1" on the face. There are the ways a=1 b=1 c=1 a=b=1  a=c=1 b=c=1 or a=b=c=1, and there are 216 total possible outcomes, so the answer is 216-7/216=209/207. (I may not have simplified)

 May 19, 2020
 #2
avatar+20883 
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You can't have a 1 on the first die:        5/6

You can't have a 1 on the second die:  5/6

You can't have a 1 on the third die:       5/6

 

Answer  =  5/6 x 5/6 x 5/6  =  125/216.

 May 19, 2020

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