Question

Two dice are thrown together. Then, the probability that the sum of numbers appearing on them is a prime number, is

• A. $\frac{5}{12}$
• B. $\frac{7}{18}$
• C. $\frac{13}{36}$
• D. $\frac{11}{36}$

Answer 1

The correct option is A

$\frac{5}{12}$

Find the required probability:

When two dice are thrown, the total number of sample spaces is $=6^2=36.$

Favourable outcomes $=\left\{(1,1),(1,2),(1,4),(1,6),(2,3),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)\right\}$

Total number of favourable outcomes $=15$

Hence, the probability of getting a sum of prime numbers $=\frac{\mathrm{number}\mathrm{of}\mathrm{favorable}\mathrm{outcomes}}{\mathrm{total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{15}{36}=\frac{5}{12}$

Hence, option (A) is correct