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6 December, 03:18

Jackson goes to the gym 0, 2, or 3 days per week, depending on work demands. The expected value of the number of days per week that Jackson goes to the gym is 2.05. The probability that he goes 0 days is 0.1, the probability that he goes 2 days is, and the probability that he goes 3 days is.

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  1. 6 December, 06:11
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    For a probability distribution the expected value is the summation of product of probabilities with their respective data values. Let x be the probability that Jackson goes gym for 2 days and y be the probability that he goes gym for 3 days.

    For the given case we have following values and their probabilities:

    0 : 0.1

    2 : x

    3 : y

    So the expected value will be = 0 (0.1) + 2 (x) + 3 (y)

    Expected value is given to be 2.05. So we can write the equation as:

    2x + 3y = 2.05 (Equation 1)

    Also for a probability distribution, the sum of probabilities must always equal to 1. So we can set up the second equation as:

    0.1 + x + y = 1

    x + y = 0.9 (Equation 2)

    From Equation 2 we can write the value of x to be x = 0.9 - y. Using this value in equation 1, we get:

    2 (0.9 - y) + 3y = 2.05

    1.8 - 2y + 3y = 2.05

    1.8 + y = 2.05

    y = 0.25

    Using the value of y in equation 2 we get value of x to be 0.65

    Therefore we can conclude that:

    The probability that Jackson goes to gym for 2 days is 0.65 and the probability that he goes to gym for 3 days is 0.25
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