A quality control inspector receives a shipment of 30 computer monitors. From the 30 monitors, the inspector randomly chooses 8 for inspection. If the probability of a monitor being defective is 0.07, what is the probability that at least one of the monitors chosen by the inspector is defective? Round to the nearest hundredth.
A)0.44
B)0.52
C)0.51
D)0.47
E)0.45

Question

Quizplus · Accepted Answer

The probability of at least one monitor being defective is easier to calculate by finding the complement, which is the probability that none of the monitors are defective. The probability of a monitor not being defective is 1 - 0.07 = 0.93. For 8 monitors, the probability that all are not defective is $0.93^8$. Subtracting this from 1 gives the probability of at least one being defective: $1 - 0.93^8 \approx 0.44$.

A Quality Control Inspector Receives a Shipment of 30 Computer