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?

No. of possible outcomes = 180 (100 50p coins + 50 ₹ 1 coins + 20 ₹ 2 coins + 10 ₹ 5 coins)

(i) No. of favourable outcomes (of getting 50p coins) = 100.

P(getting a 50p coin) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{100}{180} = \dfrac{5}{9}$.

Hence, the probability that the coin will be a 50p coin = $\dfrac{5}{9}$.

(ii) No. of favourable outcomes (of getting ₹ 5 coins) = 10.

P(getting a ₹ 5 coin) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{10}{180} = \dfrac{1}{18}$.

We know that,

Event of getting a ₹ 5 coin and event of not getting a ₹ 5 coin are complementary events.

∴ P(getting a ₹ 5 coin) + P(not getting a ₹ 5 coin) = 1

⇒ $\dfrac{1}{18}$ + P(not getting a ₹ 5 coin) = 1

⇒ P(not getting a ₹ 5 coin) = 1 - $\dfrac{1}{18}$

⇒ P(not getting a ₹ 5 coin) = $\dfrac{17}{18}$

Hence, the probability that the coin will not be a ₹ 5 coin = $\dfrac{17}{18}$.