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?
5/9
17/18
Explanation
The solution uses the classical definition of probability: P(E) = Number of favourable outcomes / Total number of equally likely outcomes, as shown in Example 1 of the provided context. The total number of coins is 180. For part (i), favourable outcomes are the 100 fifty-paise coins, so probability = 100/180 = 5/9. For part (ii), favourable outcomes are all coins except the ten ₹5 coins, i.e., 170 coins, so probability = 170/180 = 17/18. Alternatively, using the complement rule, P(not ₹5) = 1 - P(₹5) = 1 - 10/180 = 17/18.