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Question: A<sub>1</sub>, A<sub>2</sub>A<sub>3</sub> .......... A<sub>16</sub> play a knockout tournament. All ...

A1, A2A3 .......... A16 play a knockout tournament. All are equally strong. They are paired at random in each round. If A2 reaches semifinal, what is chance that A5 win

A

½

B

19/20

C

1/20

D

1/3

Answer

1/20

Explanation

Solution

A2

P(1) =

P(B/A) = 12\frac { 1 } { 2 }

P(A∩B∩C) = 15×12×12=120\frac { 1 } { 5 } \times \frac { 1 } { 2 } \times \frac { 1 } { 2 } = \frac { 1 } { 20 }