Four standard six-sided dice are rolled. What is the probability that the product of the numbers on the top faces of all four dice is a prime number? Express your answer as a common fraction.
Here's my attempt :
The only possible prime products are 2, 3 or 5
This means that 3 of the dice must show 1 and the other shows a 2, 3, or 5
The probability is
Choose any one of the four dice to show one of the primes * probability of showing three 1s on three of the dice * probability of showing one of the primes on the remaining die =
C (4,1) ( 1/6)^3 ( 3/6) =