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Math Help - Expected Probability

  1. #1
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    Expected Probability

    The manager of a boat renting company sees the weather forecasts for tomorrow.

    It claims that the probability it will rain is 0.25
    The probability that it will be cloudy and not rain is 0. 5
    The probability that it will be sunny is 0.25

    The Managers previous experience is such that during rainy days his profit is 0.
    During cloudy days his profit is $50, and during sunny day his profit is $200

    What is his expected profit for tomorrow?
    Last edited by tikimasala; June 26th 2009 at 05:10 AM.
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  2. #2
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    Quote Originally Posted by tikimasala View Post
    The manager of a boat renting company sees the weather forecasts for tomorrow.

    It claims that the probability it will rain is 0.25
    The probability that it will be cloudy and not rain is 0. 5
    The probability that it will be sunny is 0.25

    The Managers previous experience is such that during rainy days his profit is 0.
    During cloudy days his profi…t is $50, and during sunny day his profit is $200

    What is his expected pro…fit for tomorrow?
    What formula have you been taught for calculating expected value? Where are you stuck in applying it?
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  3. #3
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    Am i supposed to use the expected value of the sum of 2 discrete random variables? E(x+y) = E (x) + E (y)
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    Quote Originally Posted by tikimasala View Post
    Am i supposed to use the expected value of the sum of 2 discrete random variables? E(x+y) = E (x) + E (y)
    Surely E(Profit) = \sum (Profit) x Pr(Profit) ....
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  5. #5
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    so if i use E(Profit) = (Profit) x Pr(Profit)

    so 25% chance he makes no profit.
    50% chance he makes $50
    and 25% chance he makes $200

    im not sure where to go from here
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  6. #6
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    Quote Originally Posted by tikimasala View Post
    so if i use E(Profit) = (Profit) x Pr(Profit)

    so 25% chance he makes no profit.
    50% chance he makes $50
    and 25% chance he makes $200

    im not sure where to go from here
    No profit means profit = $0. The probability of this is 0.25. etc. Now substitute the values into the formula.

    Have you ever seen a formula like this before? Have you seen examples (in textbook or class notes) of this sort of formula? Do you know how to use this formula?

    I'm not going to do the work here. You need to start thinking.
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  7. #7
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    E(Profit) = (Profit) x Pr(Profit)

    so if i calculate it for each scenario

    i.e if its going to rain then...

    E (Profit) = $0 * 0.25
    =$0

    if its going to be cloudy then...
    E (Profit) = $50 * 0.5
    =$25

    if its going to be sunny then...
    E (Profit) = $200 * 0.25
    =$50


    i still dont see how that gives me his expected profit for tomorrow if there are 3 different scenarios.
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  8. #8
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    Quote Originally Posted by tikimasala View Post
    E(Profit) = (Profit) x Pr(Profit)

    so if i calculate it for each scenario

    i.e if its going to rain then...

    E (Profit) = $0 * 0.25
    =$0

    if its going to be cloudy then...
    E (Profit) = $50 * 0.5
    =$25

    if its going to be sunny then...
    E (Profit) = $200 * 0.25
    =$50


    i still dont see how that gives me his expected profit for tomorrow if there are 3 different scenarios.
    Do you know what the symbol \sum means? Do you realise you're meant to add each of these bits together? A minimum level of knowledge is required if effective assistance is to be given. Please, go back and thoroughly review this material.
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  9. #9
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    tikimasala, for a bit of an intuitive slant, think of "expected" as a weighted average of all the possible outcomes. The 'weights' are the probablities associated with each outcome.

    Good luck,
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