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1 May, 09:56

The probability that Mary will win a game is 0.03, so the probability that she will not win is 0.97. If Mary wins, she will be given $180; if she loses, she must pay $17. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)

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  1. 1 May, 10:26
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    Expected value of X = - 11.09

    Explanation:

    Expected profit:

    = Probability of winning * Amount she wins

    = 0.03 * $180

    = 5.4

    Expected loss:

    = Probability of loosing * Amount she paid

    = 0.97 * $17

    = 16.49

    Let X be amount of money Mary wins or loses.

    E (X) = Expected profit - Expected loss

    = 5.4 - 16.49

    = - 11.09

    Expected value of X = - 11.09

    That is expected value of loss of $11.09
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