3. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black
balls, one ball i

3. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black
balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is:

2 thoughts on “3. If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black<br />balls, one ball i”

  1. Answer:

    There are three ways draw 2 white balls and 1 black ball from the three boxes. They are:

    Scenario 1: white ball from box 1, white ball from box 2, black ball from box 3

    Scenario 2: white ball from box 1, black ball from box 2, white ball from box 3

    Scenario 3: black ball from box 1, white ball from box 2, white ball from box 3

    For box #1: P(white ball) = 3/4 = 0.75 and P(black ball) = 1/4 = 0.25

    For box #2: P(white ball) = 2/4 = 0.5 and P(black ball)= 2/4 = 0.5

    For box #3: P(white ball) = 1/4 = 0.25 and P(black ball) = 3/4 = 0.75

    The probability of scenario 1 occurring is 0.75 * 0.5 * 0.75 = 0.28125

    The probability of scenario 2 occurring is 0.75 * 0.5 * 0.25 = 0.09375

    The probability of scenario 3 occurring is 0.25 * 0.5 * 0.25 = 0.03125

    Thus, the probability that 2 white balls and 1 black ball will be drawn is P(scenario 1) + P(scenario 2) + P(scenario 3) = 0.28125 + 0.09375 + 0.03125 = 0.40625=13/32.

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