Question

You roll 2 dice. what is the probability that the sum of the dice is prime and both dice will show the number 6?

Answer 1

The probalbility is 0

Answer 2

*probability is 0 because the sum cannot be prime if both are the number 6.

Answer 3

The sum is 12 and 12 is not prime, so that doesn't work.

Answer 4

ohh I see, I feel dumb now. but thanks!

Answer 5

Probability of both dice showing 6:
The total possible outcomes of rolling 2 dice is 36. (1+1,1+2,..., 6+5, 6+6). Only one of these 36 rolls give two 6s. Hence,
Probability of both dice showing 6 is 1/36 (1 in 36).

Probability of prime:
the total number of primes between 2 (1+1) and 12 (6+6) is five (as 2,3,5,7, and 11 are prime numbers). Remember, a prime number is a number that can only be divided by 1 and itself.
The total number of ways to get 2 is 1+1 so 1 way.
The total number of ways to get 3 is 1+2 and 2+1 so 2 ways.
The total number of ways to get 5 is 1+4, 2+3 and 4+1, 3+2 so 4 ways
The total number of ways to get 7 is 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1 so 6 ways.
The total number of ways to get 11 is 5+6 and 6+5 so 2 ways.

Hence, we have 1 + 2 + 4+ 6 +2 ways to get prime rolls, which is a total of 15 ways.
Hence the probability of getting a prime is 15/36.