# Thread: Discrete Random Variable Help

1. ## Discrete Random Variable Help

Not sure why I'm getting the wrong answer for this question:
A box contains 5 salt shakers and 3 pepper shakers, each inside a plain cardboard container. If X is the number of containers opened by a person (who does not know the number of salt shakers in the box) searching for a salt shaker, make a table for the probability distribution for X.

X | Pr[X=x]
1 5/8
2 15/56
3 5/56
4 1/56

Can someone please explain why the answer is the way it is?

Thanks

2. $P(X=3)=P(pps)=\frac{3}{8}\frac{2}{7}\frac{5}{6}=\f rac{5}{56}$

3. First, do you understand what the Random Variable X is? It is "Person opens a salt shaker on the X'th try". So the probability he gets it on the first try is indeed 5/8. The probability that he gets it on the second try is the same as the probability he didn't get it on the first try (3/8) times the probability that he opens it on the second try (5/7). And so on. This is a geometric series (that you'll eventually get to), and is used to model "What is the probability it takes X tries for a success" type problems.