A fair coin is tossed until one of the two sides occurs twice in a row. The probability that the number of tosses required is even is

Options

A. `1//3`
B. `2//3`
C. `1//4`
D. `3//4`

Answer

B

Explanation

`(b)` `A={HH,HTHH,HTHTHH,…}`
or `B={TT,THTT,THTHTT,…}`
`P(A)=(1)/(2^(2))+(1)/(2^(4))+(1)/(2^(6))+.....=((1)/(4))/(1-(1)/(4))=(1)/(3)=P(B)`
`:.` Required probability `=(1)/(3)+(1)/(3)=(2)/(3)`