Question

Two players A and B are alternately throwing a coin and a die together. A player who first throws head and 6 wins the game. If A starts the game, then the probability that B wins the game is ______.

विकल्प

• `12/23`

• `11/23`

• `5/119`

• `12/119`

Answer 1

Two players A and B are alternately throwing a coin and a die together. A player who first throws head and 6 wins the game. If A starts the game, then the probability that B wins the game is `bbunderline(11/23)`.

Explanation:

Let P(getting head and 6) = `1/2`

Since, B can win the game in 2nd throw, 4th throw, 6th throw and so on. 

Hence P(B) to win the game is

= `P(barA) P(B) + P(barA) P(barB)P(barA)P(barB) + ...∞`

= `11/12 xx 1/12 + 11/12 xx 11/12 xx 11/12 xx 1/12 + ...`

= `1/12 [11/12 + (11/12)^3 + (11/12)^5 + ...]`

= `1/12 xx (11/12)/((11/12)^2)`

= `11/23`