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JEE Main20241 Feb 2024Morning ShiftMathematicsProbabilityActual

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is:

Options

  1. A2 5
  2. B2 7
  3. C1 7
  4. D1 5

Correct answer

B. 2 7

Step-by-step solution

Total Possible cases of balls in the bag could be: 2 W , 6 B , 3 W , 5 B , 4 W , 4 B , 5 W , 3 B , 6 W , 2 B The favourable case is to choose 2 W and 2 B from the bag having 4 W , 4 B So, the required probability is given by P E = C 2 4 × C 2 4 C 2 8 C 2 2 × C 2 6 C 2 8 + C 2 3 × C 2 5 C 2 8 + C 2 4 × C 2 4 C 2 8 + C 2 5 × C 2 3 C 2 8 + C 2 6 × C 2 2 C 2 8 ⇒ P E = 6 × 6 15 + 3 × 10 + 36 + 30 + 15 ⇒ P E = 36 126 ⇒ P E = 2 7

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