Question

Three coins are tossed simultaneously. Find the probability that all coins show heads if at least one of the coins shows a head.

Answer 1

We know that when three coins are tossed simultaneously the total number of outcomes = 2³ = 8

Sample space S = {(H, H, H), (H, H, T), (H, T, T), (H, T, H), (T, H, T), (T, T, H), (T, H, H), (T, T, T)}

Consider P (A) as the probability of getting 3 heads

Sample space of A = {(H, H, H)}

P (A) = 1/8

Consider P (B) as the probability of getting at least one head

Probability of one head = 1 – probability of no heads

= 1 – 1/8 = 7/8

P (B) = 7/8

Here probability that the throw is either all head or at least one head

P (A U B) = 7/8

We know that

Here the probability that all coins show heads if at least one of the coins showed a head