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Four standard six-sided dice are to be rolled. What is the probability that the product of the numbers on the top faces will be prime? Express your answer as a common fraction.

 Apr 6, 2020

Best Answer 

 #1
avatar+932 
+2

If four six-sided dice are rolled, then there are 6^4=1296 possible outcomes. Of those outcomes, the only way to get a prime number by multiplication is to have 3 of the numbers equal to 1 and the fourth number equal a prime. 

1, 1, 1, 2
1, 1, 1, 3
1, 1, 1, 5
1, 1, 2, 1
1, 1, 3, 1
1, 1, 5, 1
1, 2, 1, 1

1, 3, 1, 1
1, 5, 1, 1
2, 1, 1, 1
3, 1, 1, 1
5, 1, 1, 1

These are the 12 cases which means 12/1296=1/108 is your answer.

 

Hope it helps!

 Apr 6, 2020
 #1
avatar+932 
+2
Best Answer

If four six-sided dice are rolled, then there are 6^4=1296 possible outcomes. Of those outcomes, the only way to get a prime number by multiplication is to have 3 of the numbers equal to 1 and the fourth number equal a prime. 

1, 1, 1, 2
1, 1, 1, 3
1, 1, 1, 5
1, 1, 2, 1
1, 1, 3, 1
1, 1, 5, 1
1, 2, 1, 1

1, 3, 1, 1
1, 5, 1, 1
2, 1, 1, 1
3, 1, 1, 1
5, 1, 1, 1

These are the 12 cases which means 12/1296=1/108 is your answer.

 

Hope it helps!

HELPMEEEEEEEEEEEEE Apr 6, 2020
 #2
avatar+392 
+1

yes it definitely does

Paresh  Apr 6, 2020

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