You flip a coin until you get a total of 3 heads What is the

You flip a coin until you get a total of 3 heads. What is the expected number of flips this will take?

Solution

let X1 be the no of coin tosses untill the first head, X2 be the no of coin tosses after that untill the second head, and X3 be no of coin tosses untill the third head.

to find E(x).

where X=X1+X2+X3.by linearity expectationwe get E(X)=E(X!)+E(X2)+E(X3)

the expected coin flips untill head appear which is equal to 1/p.

therefore, E(X)=1/p+1/p+1/p=3/p