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Math Help - Basic Random Variable Question

  1. #1
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    Basic Random Variable Question

    This question is making me lose my mind. The probability of n number of events occurring is modeled by the random variable P(N = n) = 1/((n + 1)(n+2)

    And I need to find the probability of at least one happening given that not more than 4 have occurred.

    The way I did it is just by calculating P(1 <= n <= 4) = 1/3, but this isn't the correct answer. What did I do wrong?
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  2. #2
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    Re: Basic Random Variable Question

    BTW, I've considered assuming P(n >= 5) = 0, then applying some scalar k to all values of the probability, setting the sum equal to 1.

    The random variable is defined for n >= 0.
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  3. #3
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    Re: Basic Random Variable Question

    Quote Originally Posted by arcketer View Post
    This question is making me lose my mind. The probability of n number of events occurring is modeled by the random variable P(N = n) = 1/((n + 1)(n+2)

    And I need to find the probability of at least one happening given that not more than 4 have occurred.

    The way I did it is just by calculating P(1 <= n <= 4) = 1/3, but this isn't the correct answer. What did I do wrong?
    Apply Bayes' Theorem:

    \Pr(N > 0 | N \leq 4) = \frac{\Pr(N > 0 \cap N \leq 4)}{\Pr(N \leq 4)}


    and obviously \Pr(N > 0 \cap N \leq 4) = \Pr(N = 1) + \Pr(N = 2) + \Pr(N = 3) + \Pr(N = 4)
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  4. #4
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    Re: Basic Random Variable Question

    Thank you!
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