Two players Virat Kohli and Kane Williamson toss a coin alternatively, with Virat Kohli beginning the game. The players who first throw a head are deemed to be the winner. Kane Williamson's coin is fair and Virat Kohli 's is biased and has a probability p showing a head. Find the value of p so that the game is equiprobable to both the players.

Two players Virat Kohli and Kane Williamson toss a coin alternatively, with Virat Kohli beginning the game. The players who first throw a head are deemed to be the winner. Kane Williamson's coin is fair and Virat Kohli 's is biased and has a probability p showing a head. Find the value of p so that the game is equiprobable to both the players. Correct Answer 1/3

Calculation:

⇒ Virat Kohli (VK) wins if he gets head in the first trial or in third and so on.

⇒ P(VK) = p + (1 - p) × 1/2 × p + (1 - p) × 1/2 × (1 - p) × 1/2 × p +...∞

⇒ This is an infinite G.P. of first term p and common ratio (1 - p)/2 = p/(1 – ((1 - p)/2)) = (2p)/(p + 1)

⇒ According to given condition

⇒ P(VK) = P(KW)

⇒ 2p/(1 + p) = 1 – 2p/(p + 1)

⇒ (4p)/(1 + p) = 1

⇒ p = 1/3