Question

A piggy bank contains hundred 50 paise coins, fifity ₹1 coins, twenty ₹2 coins and ten ₹5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, find the probability that the coin which fell

(i) will be a 50 paise coin
(ii) will be of value more than ₹1
(iii) will be of value less than ₹5
(iv) will be a ₹1 or ₹2 coin [CBSE 2014]

Answer 1

Total number of coins = 100 + 50 + 20 + 10 = 180

So, the total number of outcomes is 180.

(i) Number of 50 paise coins = 100

So, the favourable number of outcomes are 100.

∴ P(the coin which fell is a 50 paise coin) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{100}{180}=\frac{5}{9}$

(ii) A coin of value more than ₹1 can be ₹2 or ₹5 coin.

Number of ₹2 or ₹5 coins = 20 + 10 = 30

So, the favourable number of outcomes are 30.

∴ P(the coin which fell has value more than ₹1 ) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{30}{180}=\frac{1}{6}$

(iii) A coin of value less than ₹5 can be 50 paise or ₹1 or ₹2 coin.

Number of 50 paise or ₹1 or ₹2 coins = 100 + 50 + 20 = 170

So, the favourable number of outcomes are 170.

∴ P(the coin which fell has value less than ₹5 ) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{170}{180}=\frac{17}{18}$

(iv) Number of ₹1 or ₹2 coins = 50 + 20 = 70

So, the favourable number of outcomes are 70.

∴ P(the coin which fell will be a ₹1 or ₹2 coin ) = $\frac{\mathrm{Favourable}\mathrm{number}\mathrm{of}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}}=\frac{70}{180}=\frac{7}{18}$