A manufacturing company has a 2% defect rate and seven items are chosen at random. What is the probability that one will have a defect?

Answer 1

As it is worded here, the question is ambiguous. You should specify whether you are to calculate the probability that "at least one" has a defect or the probability that "exactly one" has a defect. Those are two different events, with two different probabilities.

For "at least one" it is easiest to calculate the probability that there are no defective items, then subtract that probability from 1:

1 - (.98)⁷ ≈ 13%

For "exactly one" we use the binomial distribution:

(⁷₆) · (.98)⁶(.02)¹ ≈ 12.4%