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: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.