Question

The probability of throwing a number greater than 2 with a fair die is [CBSE 2011]

(a) $\frac{2}{5}$
(b) $\frac{5}{6}$
(c) $\frac{1}{3}$
(d) $\frac{2}{3}$

Answer 1

​Total number of outcomes = 6.

Out of the given numbers, numbers greater than 2 are 3, 4, 5 and 6.

Numbers of favourable outcomes = 4.

∴ P(getting a number greater than 2) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{4}{6}=\frac{2}{3}$

Thus, the probability of getting a number greater than 2 is $\frac{2}{3}$.

Hence, the correct answer is option (d).