Multiple choice

A bag contains 5 white balls and 3 black balls. 4 balls are successively drawn from it without replacement. The probability that balls of different colours are alternately drawn is

  1. 1/196

  2. 2/7

  3. 1/7

  4. 13/56

  5. 3/7
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C Correct answer
AI explanation

To draw the 4 balls alternately, they must be drawn in the order white, black, white, black or black, white, black, white. The probability of the first sequence is (5/8) multiplied by (3/7) multiplied by (4/6) multiplied by (2/5), which equals 1/14. The probability of the second sequence is (3/8) multiplied by (5/7) multiplied by (2/6) multiplied by (4/5), which also equals 1/14. Adding the probabilities of these two mutually exclusive sequences gives 1/14 + 1/14 = 2/14, which simplifies to 1/7.

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