Question

Brown Manufacturing makes auto parts that are sold to

auto dealers. Last week the company shipped 25 auto parts to a dealer.

Later, it found out that 5 of those parts were defective. By the time the

company manager contacted the dealer, 4 auto parts from that shipment

had already been sold. What is the probability that

(a) 3 of those 4 parts were good parts?

(b) all the 4 parts are good?

Answer 1

(a) $P(X=3)=\frac{C_{20}^3C_5^1}{C_{25}^4}=\frac{5700}{12650}=\frac{114}{253}\approx0.4506.$

(b) $P(X=4)=\frac{C_{20}^4}{C_{25}^4}=\frac{4845}{12650}=\frac{969}{2530}\approx0.3830.$