A fair coin is continually flipped Compute the expected numb

A fair coin is continually flipped. Compute the expected number of flips until the following pattern appears TTT. E(number of flips until TTT) =

assume the expected number of tosses is E.

Prob first toss is H =1/2

given that the first toss if H , no of tosses require = 1+ E

Similarly,

Prob first toss is T and second is H =1/4

given that the first toss if T and second is H, no of tosses require = 2+ E

Prob first toss is T and second is T and third is H =1/8

given that the first toss if T and second is T and third is H, no of tosses require = 3+ E

Prob first toss is T and second is T and third is T =1/8

given that the first toss if T and second is T and third is T, no of tosses require = 3

All these events are mutually exclusive and exhaustive

So E = 1/2*(1+E) + 1/4*(2+E) + 1/8*(3+E) + 1/8*(3)

1/8 E = 14/8

E = 14