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.

Answer: 0.55858

If at least 500 items are checked to find two defectives,

then the first 499 contained exactly one defective or no defectives.

. .

. .

Therefore: .