+385 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.
+934 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!
+934 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!
