Question

A piggy bank contains hundred 50p coins, fifty ₹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, what is the probability that the coin
(i) will be a 50 p coin?
(ii) will not be a ₹5 coin?

Answer 1

Total number of coins in a piggy bank = 100 + 50 + 20 + 10 = 180
(i) Number of 50 p coins = 100
$\text{Probability}\ \text{ of}\ \text{ getting}\ \text{ a }\ \text{50}\ \text{ coin}=\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}$
$=\frac{100}{180}=\frac{5}{9}$

(ii) Number of Rs 5 coins = 10
$\text{Probability}\ \text{ of}\ \text{ getting}\ \text{ a }\ \text{5}\ \text{ coin}=\frac{\text{Number}\ \text{ of} \ \text{favourable}\ \text{ outcomes}}{\text{Number}\ \text{ of }\ \text{total }\ \text{possible} \ \text{outcomes}}$
$=\frac{10}{180}=\frac{1}{18}$
Probability of not getting a Rs 5 coin $=1-\frac{1}{18}$
$=\frac{17}{18}$