Two six sided dice are rolled. What is the probability that the sum is a prime number?

Apr 13, 2018

Probability of getting sum as a prime number is $\frac{5}{12}$

Explanation:

Total number of possible outcome is $T = 6 \cdot 6 = 36$

Prime numbers are $2 , 3 , 5 , 7 \mathmr{and} 11$

Favorable outcome is

$F = 15 \left(11 , 12 , 14 , 16 , 21 , 23 , 25 , 32 , 34 , 41 , 43 , 52 , 56 , 61 , 65\right)$

Probability of getting sum as a prime number is

$P \left({S}_{p}\right) = \frac{F}{T} = \frac{15}{36} = \frac{5}{12}$ [Ans]