Question

Two dice are tossed. The probability that the total score is a prime number is

• A. $\frac{1}{6}$
• B. $\frac{5}{12}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

The correct option is B

$\frac{5}{12}$

Find the probability of the mentioned situation:

If the two dice rolled simultaneously, then the size of the sample space$=36$

Let $A$ be the event of the total score is a prime number

Now, the size of the event $A$$=\left\{\right(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5\left)\right\}$ $=15$

So, the probability of getting a total score which is a prime number$=\frac{\mathrm{number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{number}\mathrm{of}\mathrm{total}\mathrm{outcomes}}=\frac{15}{36}=\frac{5}{12}$

Hence, the correct option is (B).