# Need help with geometric pmf

#### Dichotomous

##### New Member
Hi all,
Here's the problem:

Let X be the number of accidents per week in a factory. Let the probability mass function of X be

f(x) = 1/(x+1) - 1/(x+2), x = 0,1,2,....

Find the conditional probability of X >= 4, given that X>=1.

Thanks!

#### Dason

Hi! :welcome: We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

#### Dichotomous

##### New Member
Hi all,
Here's the problem:

Let X be the number of accidents per week in a factory. Let the probability mass function of X be

f(x) = 1/(x+1) - 1/(x+2), x = 0,1,2,....

Find the conditional probability of X >= 4, given that X>=1.

Thanks!
Thanks for the info Dason.

My first thought is to find P(X >=4) for f(x) and P(X >= 1) for f(x). Then I take the results and compute the conditional probability for f(x) P(X >= 4 | X >= 1).

So, P(X >= 4) is equivalent to the SUM (with k=4 to infinity) f(x)^k - f(x=0) - f(x=1)- f(x=2) - f(x=3).
Similarly, (P >= 1) = SUM (w/ k=1 to infinity) f(x)^k - f(x=0).

Is this reasoning correct so far?