Question

Six faces of an unbiased die are numbered with $2,3,5,7,11$ and $13$. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is

• A. $\frac{5}{18}$
• B. $\frac{5}{36}$
• C. $\frac{13}{18}$
• D. $\frac{25}{36}$

Answer 1

Answer: (A)

$\frac{5}{18}$

The sum on the uppermost faces of the dice is an odd number. Hence exactly one of the two numbers on the uppermost face is $2$. So the different possible combinations are $(2,3),(2,5),(2,7),(2,11),(2,13),(3,2),(5,2),(7,2),(11,2)$ and $(13,2)$
Total required combinations $=10$
The probability that the sum on the uppermost faces of the dice is an odd number is $=\frac{10}{36}=\frac{5}{18}$