In a game, winning is defined by the outcome 6 on a die. Three players A, B, C play this game. The die is first
thrown by C, followed by A, and then B. If the order of throwing the die is same for all rounds, then the
probability that A wins the game, is
60
911
25
91
66
91
30
91
Answers
Given : In a game, winning is defined by the outcome 6 on a die.
Three players A, B, C play this game. The die is first
thrown by C, followed by A, and then B. If the order of throwing the die is same for all rounds,
To Find : probability that A wins the game,
Solution:
Probability that C wins = (1/6) in 1st round
A wins if C does not win
Probability that A wins in 1st round = (5/6) * (1/6) = 5/36
B wins if A and C does not win
Probability that B wins in 1st round = (5/6) * (5/6) (1/6) = 25/216
In next round probabilities are multiplied by (125/216) as no one wins in previous round
Probability That A wins =
a = 5/36 r = 125/216 and GP is infinte
S =a/(1 - r)
= (5/36) /( 1 - 125/216)
= 216 * 5 / ( 36 * 91)
= 30/91
30/91 is the Probability that A wins
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