Question

Cards bearing numbers 2, 3, 4, ..., 11 are kept in a bag. A card is drawn at random from the bag. The probability of getting a card with a prime number is [CBSE 2012]

(a) $\frac{1}{2}$
(b) $\frac{2}{5}$
(c) $\frac{3}{10}$
(d) $\frac{5}{9}$

Answer 1

​Total number of cards = 10.

Out of the given numbers, prime numbers are 2, 3, 5, 7 and 11.

Numbers of favourable outcomes = 5.

∴ P(getting a prime number) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{5}{10}=\frac{1}{2}$

Thus, the probability of getting a card with a prime number is $\frac{1}{2}$.

Hence, the correct answer is option (a).