A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is `3//16` b. `5//32` c. `3//16` d. `1//8`

Options

A. `3//16`
B. `5//32`
C. `3//16`
D. `1//8`

Answer

B

Explanation

Let H donote thenhead, T the tail and any of the head or tail. Then, `P(H)=1//2,P(T)=1//2andP(""^(**))=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.`