Question

A tire company produced a batch of 6 comma 700 tires that includes exactly 250 that are defective.
a. if 4 tires are randomly selected for installation on a​ car, what is the probability that they are all​ good?
b. if 100 tires are randomly selected for shipment to an​ outlet, what is the probability that they are all​ good? should this outlet plan to deal with defective tires returned by​ consumers?

Answer 1

the probability that if you pick only one, it's defective, is 250/6700

Therefore, the probability that one is not defective is 6450/6700

a. You want all 4 to not be defective: (6450/6700)^4

b. all 100 have to be not defective: (6450/6700)^100

If you type this into a calculator, you will get about 0.022, so a probability of 2 % that all of them are not defective. As this is a very small probability, the outlet should plan with returned tires.