Multiple choice

A bag contains 10 white and 6 black balls. 4 balls are successively drawn without replacement. What is the probability that they are alternatively of different colours?

  1. 81/728

  2. 90/728

  3. 18/728

  4. 638/728

  5. 1/728
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total ways to draw 4 balls = 16C4 = 1820. Favorable ways: (W,B,W,B) or (B,W,B,W). W,B,W,B = (10/16)(6/15)(9/14)(5/13) = 2700/43680. B,W,B,W = (6/16)(10/15)(5/14)(9/13) = 2700/43680. Total = 5400/43680 = 90/728.

AI explanation

The bag contains 16 balls total, and the probability can be calculated using the general multiplication theorem for dependent events. The probability of drawing white, black, white, black in that order is (10/16) times (6/15) times (9/14) times (5/13), which equals 45 out of 728. The probability of drawing black, white, black, white in that order is (6/16) times (10/15) times (5/14) times (9/13), which also equals 45 out of 728. Adding these two mutually exclusive sequences gives 90/728.

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