Multiple choice

A bag contains 3 white and 3 red balls, pairs of balls are drawn without replacement until the bag is empty. The probability that each pair consist of one white and one red ball is-

  1. $\dfrac{2}{5}$
  2. $\dfrac{4}{10}$
  3. $\dfrac{5}{10}$
  4. $\dfrac{6}{10}$
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A Correct answer
AI explanation

The bag contains 6 balls in total, and drawing them in pairs without replacement until empty means forming 3 pairs. The total number of ways to choose the first pair from 6 balls is the combination of 6 taken 2 at a time, which is 15. The number of ways to choose one white ball from 3 and one red ball from 3 is 3 multiplied by 3, which equals 9. The probability that the first pair consists of one white and one red ball is 9/15. For the second pair, the probability of drawing one white and one red ball from the remaining 4 balls is 4/6. For the third pair, the probability is 2/2. The total probability is 9/15 multiplied by 4/6 multiplied by 2/2, which is 3/5 multiplied by 2/3 multiplied by 1, giving 6/15. This simplifies to 2/5. The result is 2/5.

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