Question

A piggy bank contains hundred 50 p coins, seventy ₹1 coin, fifty ₹2 coins and thirty ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin

(i) will be a ₹1 coin?
(ii) will not be a ₹5 coin?
(iii) will be a 50 p or a ₹2 coin?

Answer 1

Number of 50 p coins = 100.
Number of ₹1 coins = 70.
Number of ₹2 coins = 50.
Number of ₹5 coins = 30.

Thus, total number of outcomes = 250.

(i) Let E₁ be the event of getting a ₹1 coin.

Number of favourable outcomes = 70.

∴ P(getting a ₹1 coin) = P(E₁) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_1}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{70}{250}=\frac{7}{25}$

Thus, the probability that the coin will be a ₹1 coin is $\frac{7}{25}$.

(ii) Let E₂ be the event of not getting a ₹5 coin.

Number of favourable outcomes = 250 − 30 = 220

∴ P(not getting a ₹5 coin) = P(E₂) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_2}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{220}{250}=\frac{22}{25}$

Thus, the probability that the coin will not be a ₹5 coin is $\frac{22}{25}$.

(iii) Let E₃ be the event of getting a 50 p or a ₹2 coin.

Number of favourable outcomes = 100 + 50 = 150

∴ P(getting a 50 p or a ₹2 coin) = P(E₃) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{outcomes}\mathrm{favourable}\mathrm{to}{\mathrm{E}}_3}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{150}{250}=\frac{3}{5}$

Thus, the probability that the coin will be a 50 p or a ₹2 coin is $\frac{3}{5}$.