Question

17 cards numbered 1, 2, 3, 4, .... ,17 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an odd number (ii) a number divisible by 5.

Answer 1

Total number of cards = 17

(i) Let E₁ be the event of choosing an odd number.

These numbers are 1, 3, 5, 7, 9, 11, 13, 15 and 17.

∴ P(getting an odd number) = P(E₁) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_1}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{9}{17}$

Thus, the probability that the card drawn bears an odd number is $\frac{9}{17}$.

(i) Let E₂ be the event of choosing a number divisible by 5.

These numbers are 5, 10 and 15.
∴ P(getting a number divisible by 5) = P(E₂) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_2}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{3}{17}$

Thus, the probability that the card drawn bears a number divisible by 5 is $\frac{3}{17}$.