Question

A, B, C throw a fair coin one by one in the order A, B, C, A, B, C .... whoever throws head before the other is the winner. Then the probability that C wins is

• A. 2/7
• B. 3/7
• C. 4/7
• D. 1/7

Answer 1

Answer: (D)

1/7

Answer 2

P(3) = P₃ + P₆ + P₉ + .......... ∞

= $\left( \frac { 1 } { 2 } \right) ^ { 2 } \cdot \frac { 1 } { 2 } + \left( \frac { 1 } { 2 } \right) ^ { 5 } \cdot \frac { 1 } { 2 } + \left( \frac { 1 } { 2 } \right) ^ { 8 } \cdot \frac { 1 } { 2 } \ldots \ldots \ldots \ldots \infty = \frac { \left( \frac { 1 } { 2 } \right) ^ { 3 } } { 1 - \left( \frac { 1 } { 2 } \right) ^ { 3 } } = \frac { \frac { 1 } { 8 } } { 1 - \frac { 1 } { 8 } } = \frac { 1 } { 7 }$ .