# Help with negative binomial distributions

mintsharpie
One of the questions in my probability homework reads:

X denotes a negative binomial random variable, with p = 0.6 Find P(X ≥ 3) for a) r = 2 and b) r = 4.

According to my teacher, the answers are 0.1792 and 0.45568, respectively, but I can't for the life of me figure out how he got them. I tried finding P(X ≥ 3) by turning it into 1 - P(X ≤ 2) and then calculating p(2), p(1), and p(0), but I kept getting 0 for my answer, which obviously isn't correct.

Can someone please help me solve this problem, or explain to me how I would go about solving it? I'm really confused.

Thanks.

## Answers and Replies

Homework Helper
Gold Member
One of the questions in my probability homework reads:

X denotes a negative binomial random variable, with p = 0.6 Find P(X ≥ 3) for a) r = 2 and b) r = 4.

According to my teacher, the answers are 0.1792 and 0.45568, respectively, but I can't for the life of me figure out how he got them. I tried finding P(X ≥ 3) by turning it into 1 - P(X ≤ 2) and then calculating p(2), p(1), and p(0), but I kept getting 0 for my answer, which obviously isn't correct.

Can someone please help me solve this problem, or explain to me how I would go about solving it? I'm really confused.

Thanks.

Remember that the negative binomial models the number of Bernoulli trials up to and including the rth success. Therefore $p(x) > 0$ only for $x \ge r$.

If r = 2, then p(0) and p(1) are obviously zero, so your first calculation should just be 1 - p(2), which isn't zero and isn't his answer either. And if r = 4, obviously P(X ≥ 3) = 1 since you can't have 4 successes in less than three trials. Time to ask your teacher what's going on.