# Math Help - Basic Random Variable Question

1. ## 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?

2. ## 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.

3. ## Re: Basic Random Variable Question

Originally Posted by arcketer
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 $\Pr(N > 0 \cap N \leq 4) = \Pr(N = 1) + \Pr(N = 2) + \Pr(N = 3) + \Pr(N = 4)$

Thank you!