Consider a game played by 10 people in which each flips a fair up coin at the same time. If all but one of the coins comes up the same, then the odd persons wins (e.g., if there are nine tails and one head then head wins). If such a situation does not occur, the players flips again. Find the probability that game is settled on or after nth toss.

Explanation

(i) the probability that one gets tail and nine get head is `""^(10)C_(1)1/2((1)/(2))^(9)`
(ii) The probability that one gets head and nine hets tail is `""^(10)C_(1)1/2((1)/(2))^(9)`
Hence, probability that the game is settled is
`2xx""^(10)C_(1)1/2((1)/(2))^(9)=(5)/(2^(8))`
If the game is not settled in the first toss, its probability is `1-5//2^(8).` If the game is not settled in the second toss, its probability is `(1-5//2^(8))^(n-1),` whihc is equal to the probability that the game is settled on or after the nth toss.