A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is
Let H denote the head, T the tail and * any of the head or tail.
Then, P(H) = 1/2, P(T) = 1/2 and P(*) = 1. For at least four consecutive heads, we should have any of the following patterns:
Probability | |
(i) H H H H * * * | |
(ii) T H H H H * * | |
(iii) * T H H H H * | |
(iv) * * T H H H H |
Since all the above cases are mutually exclusive, the probability of getting at least four consecutive heads (on adding) is 1/16 + 3/32 = 5/32.