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23 May, 11:38

8. A coin is tossed. If it shows heads, a marble is drawn from Box 1, which contains one white and one black

marble. If it lands tails, a marble is drawn from Box 2, which contains two white and one black marble. Find:

a) P (black coin fell heads)

b) P (white coin fell tails)

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  1. 23 May, 13:10
    0
    a) 0.25

    b) 0.34

    Step-by-step explanation:

    There are two levels of probability to consider; the probability of the coin being heads or tails, and after that the probability of choosing a white or black marble (depending on which box is chosen).

    The probability of heads is 0.5 and the probability of tails is 0.5.

    For Box 1 (i. e. coin was heads), the probability of choosing a white marble is 0.5, and the probability of choosing a black marble is 0.5.

    For Box 2 (i. e. coin was tails), the probability of choosing a white marble is 0.67, and the probability of choosing a blck marble is 0.33.

    The probability that the coin fell heads AND the marble is black is 0.5 x 0.5 = 0.25

    The probability that the coin fell tells AND the marble is white is 0.5 x 0.67 = 0.34.

    Remember, "and" means multiply probabilities (for independent events).
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