Q.

In a knockout tournament, 2n equally skilled players; S1, S2, .…, S2n are participating. In each round, players are divided in pairs at random and winner from each pair moves to the next round. If S2 reaches the semi-final, then the probability that S1 wins the tournament is 184. The value of n is ________.

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answer is 6.

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Detailed Solution

Given S2 reaches the semi-finals.Since all other players (2n - 1) are equally likely to win the finals with probability p.∴     2n−1p+14=1⇒     2n−1p=34⇒ p=342n−1If p=184, then∴    184=342n−1⇒    2n−1=63⇒     2n=64⇒     n=6
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In a knockout tournament, 2n equally skilled players; S1, S2, .…, S2n are participating. In each round, players are divided in pairs at random and winner from each pair moves to the next round. If S2 reaches the semi-final, then the probability that S1 wins the tournament is 184. The value of n is ________.