Two six-sided dice are tossed.Find the probability that the sum is prime or even.

Question

Quizplus · Accepted Answer

We can find the number of ways to get a prime or even sum by computing the complementary probability (i.e. the probability of rolling an odd non-prime sum), and then subtracting from 1.

To get an odd non-prime sum, we can either roll an odd number on the first die (3 ways), and a non-prime even number on the second die (2 ways), or an even number on the first die (3 ways), and a non-prime odd number on the second die (3 ways).

So there are a total of 3 x 2 + 3 x 3 = 15 ways to get an odd non-prime sum out of 6 x 6 = 36 possible outcomes when rolling two dice.

Therefore, the probability of getting a prime or even sum is 1 - 15/36 = 7/12, which corresponds to choice B.

Two Six-Sided Dice Are Tossed