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10 February, 08:57

Ben rolls 5 fair 12-sided dice. the 12 faces of each die are numbered from 1 to 12. what is the probability that exactly two of the dice show an even number?

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  1. 10 February, 12:55
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    We will use the Binomial Probability formula to find the answer

    The formula is given by ⁿCₓ (p) ˣ (1-p) ⁿ⁻ˣ

    Where:

    n, the number of trials = 5

    x, the number of success that we aim = 2

    p, the probability of success = 0.5 ⇒ there are six out of twelve numbers on the dice that are even

    Substitute these values into the formula, we have

    P (2) = ⁵C₂ (0.5) ² (1-0.5) ⁵⁻²

    P (2) = ⁵C₂ (0.5) ² (0.5) ³

    P (2) = 0.3125
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