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Math Help - Probability that profit will be $8000 or more...

  1. #1
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    Probability that profit will be $8000 or more...

    Suppose you have $100,000 to invest in stocks. If you invest $1000 in any particular stock your profit will be $200, $100, $0 or -$100 (a loss), with probability 0.25 each. There are 100 different stocks you can choose from, and they all behave independently of each other. Consider the 2 cases: (1) Invest $100,000 in one stock. (2) Invest $1000 in each of 100 stocks.

    a) For case (1) find the probability that your profit will be $8000 or more
    b) Do the same for case (2)

    So I'm thinking for a) if you invest all $100,000 in one stock it would raise the profits to $20,000, $10,000, $0, or -$10,000, but I don't know how you'd figure out it it'd be $8000 or more? Please help!
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  2. #2
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    Quote Originally Posted by bart203 View Post
    Suppose you have $100,000 to invest in stocks. If you invest $1000 in any particular stock your profit will be $200, $100, $0 or -$100 (a loss), with probability 0.25 each. There are 100 different stocks you can choose from, and they all behave independently of each other. Consider the 2 cases: (1) Invest $100,000 in one stock. (2) Invest $1000 in each of 100 stocks.

    a) For case (1) find the probability that your profit will be $8000 or more
    b) Do the same for case (2)

    So I'm thinking for a) if you invest all $100,000 in one stock it would raise the profits to $20,000, $10,000, $0, or -$10,000, but I don't know how you'd figure out it it'd be $8000 or more? Please help!
    In the second case your profit will be the sum of 100 independently identically distributed random variables, so what do you know about such a sum?

    CB
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