Question

A biased coin with probability p, 0<p<1 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.

• A. 1/3
• B. 2/3
• C. 2/5
• D. 3/5

Answer 1

Answer: (A)

1/3

Answer 2

Let Since head appears first time in an even throw i.e., 2 or 4 or 6 etc.,

\ 2/5 =

Ž $\frac { 2 } { 5 } = \frac { q p } { 1 - q ^ { 2 } } \Rightarrow \frac { 2 } { 5 } = \frac { ( 1 - p ) p } { 1 - ( 1 - p ) ^ { 2 } } = \frac { 1 - p } { 2 - p }$

Ž $2 ( 2 - p ) = 5 ( 1 - p ) \Rightarrow p = 1 / 3$