An experiment consists of tossing 5 fair (not weighted) coins, except one of the coins has heads on both sides. Compute the probability of obtaining exactly 4 heads.

Answer 1

Let, P(E) be the probability of an event E where P(E) is defined as P(E) = No. of favorable outcomes / Total number of outcomes. = n(E) / n(S).

Let, H be the head and T be the tail, then total number of outcomes or Sample space will be n(S) = {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH, THHHH} = 6

Number of favourable outcomes or n(E) = {HHHHT, HTHHH, HHTHH, HHHTH, HHHHT} = 5 (Here, you can see that we have 4 Heads.

So, P(E) = 5/6 (this is the required answer).