8 players \( P_{1}, P_{2}, P_{3}, \ldots, P_{8} \) play a knock out...

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8 players \( P_{1}, P_{2}, P_{3}, \ldots, P_{8} \) play a knock out tournament.
It is known that all the players are of equal strength. The
\( \mathrm{P} \) tournament is held in three rounds where the players

W are paired at random in each round. If it is given that \( P_{1} \) wins in the third round. If \( p \) be the probability that \( P_{2} \) loses in the second round, then the value of \( 7 p \) is
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