Question

A factory receives a shipment of 1,000 transistors. The supplier knows that 50 out of the 1,000 transistors are defective. The factory will test a sample of 100 out of the 1,000 transistors, and reject the shipment if too many transistors in the sample are defective. First, assume that the 100 transistors in the sample are chosen in sequence, with replacement from the shipment of 1,000 transistors.

(a) what is the probability that at least one transistor in the sample is defective?

(b) what is the probability that exactly 4 transistors in the sample are defective? Now, rather than the assumption above, assume that the 100 transistors in the sample are chosen as an unordered set, without replacement from the shipment of 1,000 transistors.

(c) how many different unordered samples of 100 transistors can be chosen?

(d) what is the probability that exactly 4 transistors in the sample are defective?

Answer 1