A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets: (i) at least one head? (ii) at most one head?
A man tosses two different coins (one of Rs 2 and another of Rs 5) simultaneously. What is the probability that he gets: (i) at least one head? (ii) at most one head?

Solution:

We know that,

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

So, n(S) = 4

(i) The outcomes favourable to the event E, ‘at least one head’ are {(H, H), (H, T), (T, H)}

So, the number of outcomes favourable to E is 3 = n(E)

Hence, P(E) = n(E)/ n(S) = ¾

(ii) The outcomes favourable to the event E, ‘at most one head’ are {(T, H), (H, T), (T, T)}

So, the number of outcomes favourable to E is 3 = n(E)

Hence, P(E) = n(E)/ n(S) = 3/4