Elaine rolls 2 fair dice. What is the probability of both dice showing a prime number?

The prime numbers are 2, 3, and 5.

The numbers that aren't prime are 1, 4, and 6.

 

The probability that the first die shows a prime number is:  3/6.

The probability that the second die shows a prime number is:  3/6.

 

The probability that both show prime numbers is:  3/6 x 3/6  =  ...

Roll 2 fair dice = 36 outcomes. Outcomes with both dice showing prime number = {(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)}

P(both dice showing a prime number) = 9/36 = 1/4.