Probability of computer chips being defective In a factory that makes computer chips, all chips that are made are 2% defective. An inspector comes and randomly inspects 4 chips from the conveyor belt. What is the probability of at _least_ one of the 4 chips being defective? I have the solution, but I don't quite understand it. Here it is: * * * $P($at least one defective$)$ $=$ $1 - $ $P($all 4 not defective$)$ $P($at least one defective$)$ $=$ $1 - $ $(0.98)^4$ $P($at least one defective$)$ $≈$ $1 - $ $0.922$ $P($at least one defective$)$ $≈$ $0.078$ Can someone explain this to me?

In general, $$P(\text{event happens}) = 1 - P(\text{event doesn't happen}).$$

Here, the opposite (complement) of "at least one chip is defective" is "all four chips are not defective." This gives the first line of the solution.

To compute the probability of "all four chips are not defective," you use the [tacit] assumption that the defectiveness of each chip being independent of other chips, to obtain $$P(\text{all 4 chips not defective}) = P(\text{chip not defective}) \cdot P(\text{chip not defective}) \cdot P(\text{chip not defective}) \cdot P(\text{chip not defective}) = (0.98)^4.$$