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A chess match between 2 players A and B is won by whoever first wins a total of 2 games. Probability of A winning, drawing and losing any particular game is 1 7 , 2 7 and 4 7 respectively (the games are independent). If the probability that A wins the match in the fourth game is p , then 343 p is equal to

Options

  1. A60
  2. B30
  3. C60 7
  4. D30 7

Correct answer

C. 60 7

Step-by-step solution

A win match in 4 t h game ⇒ A win one game in first 3 games, D D , L D , D L are possibilities for remaining 2 matches. Hence, the required probability = C 3 1 1 7 2 7 × 2 7 + 2 7 × 4 7 + 4 7 × 2 7 × 1 7 = 60 7 4 = 60 2401 = p ⇒ 343 p = 60 7

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