A biased coin with probability p, `0ltplt1` of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is 2/5, then p equals

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(2)/(5)`
D. `(3)/(5)`

Answer

A

Explanation

(a) Let q=1-p. Since, head appears first time in an even throw i.e. 2 or 4 6, etc.
`:. " " (2)/(5)=qp+q^(3)p+q^(5)p+……`
`rArr " " (2)/(5)=(qp)/(1-q^(2)) rArr (2)/(5)=((1-p)p)/(1-(1-p)^(2))=(1-p)/(2-p)`
`rArr 2(2-p)=5(1-p) rArr p=(1)/(3)`