1. ## Negative Binomial

Ok, so when I try solved the attached problem I don't know how to come up with the right answer which is : 0.55858

My way of solving the problem is the following:

x=50 to infinity = 499(0.003)^2 (0.997)^498 + 500(0.003)^2(0.997)^499

Do I need to something like-> (0.003)^2(0.997)^498 / (1 - 0.997) ?

2. Hello, MathRules!

The probability that a machine produces a defective item is 0.003.
Each item is check as it is produced.
Assume that these are independent trials.
Compute the probability that at least 500 items must be checked
to find two items that are defective.

. . $P(\text{1 d{e}f}) \:=\:{499\choose1}(0.997)^{498}(0.003)^1 \:\approx\: 0.33528$
. . $P(\text{no d{e}f}) \:=\:(0.997)^{499} \:\approx\:0.22330$
Therefore: . $P(\text{1 or 0 d{e}f}) \:=\:0.33528 + 0.22330 \:=\:0.55858$