A man tosses two different coins (one of ₹ 2 and another of ₹ 5) simultaneously. What is the probability that he gets :

(i) at least one head ?

(ii) at most one head ?

We know that,

When two coins are tossed simultaneously, the possible outcomes are {(H, H), (H, T), (T, H), (T, T)}

∴ No. of possible outcomes = 4.

(i) The outcomes favourable to event, 'at least one head' are {(H, H), (H, T), (T, H)}.

∴ Number of favourable outcomes = 3

P(getting at least one head) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{4}$.

Hence, the probability that he gets at least one head = $\dfrac{3}{4}$.

(ii) The outcomes favourable to event, 'at most one head' are {(H, T), (T, H), (T, T)}.

∴ Number of favourable outcomes = 3

P(getting at most one head) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{3}{4}$.

Hence, the probability that he gets at most one head = $\dfrac{3}{4}$.