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.

Paresh Apr 6, 2020

#1**+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!

HELPMEEEEEEEEEEEEE Apr 6, 2020

#1**+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