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A bag contains 5 balls of unknown colours. A ball is drawn at random from it and is found to be red. Then the probability that all the balls in the bag are red, is

Options

  1. A1 2
  2. B1 4
  3. C2 5
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

Let R i ( i = 1 , 2 , 3 , 4 , 5 ) denotes 1 , 2 , 3 , 4 or 5 red balls in the bag. Let R represent the ball drawn is red, then P ( R 1 ) = P ( R 2 ) = P ( R 3 ) = P ( R 4 ) = P ( R 5 ) = 1 5 a n d P R R 1 = 1 5 , P R R 2 = 2 5 , P R R 3 = 3 5 , P R R 4 = 4 5 P R R 5 = 1 ∴ P R 5 R = P ( R 5 ) ⋅ P R R 5 ∑ i = 1 5 P ( R i ) ⋅ P R R i = 1 1 + 1 5 + 2 5 + 3 5 + 4 5 = 5 15 = 1 3

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