Hello tutors, may I please get help solving the following prob// stat problems ? Thank you.

1) Suppose that a large university contains 10 percent mountain climbers. If four students are randomly sampled from the university, what is the probability that exactly one student is a mountain climber?

a. 0.057

b. 0.1

c. 0.2916 d. 0.001 e. 0.3439

2) A purchaser of electrical components buys them in lots of size 10. It is his policy to inspect 3 components randomly from a lot and to accept the lot only if all 3 arenondefective. If 30 percent of the lots have 4 defective components and 70 percent have only 1, what proportionof lots does the purchaser reject?

Notice that you must use the law of total probability in this problem. The conditional probabilities are calculated with the hypergeometric, since you are drawing from a rather small lot, 10, so you can not make the assumption that the lot is large.

Calculate

P(accept) = P(accept|lot 1)P(lot1) + P(accept|lot 2)P(lot 2) by law of total probability

Then calculate, by complement rule,

P(reject=1-P(accept)

a. 54%

b. 46%

c. 33%

d. 90%

3) A system with 6 independent components is such that the system will fail if at least one of the individual components fail. The probability that a component fails is 0.02. Let A be the event that the system fails. What is the probability of A ?

a. 0.6672142

b. 0.8858424 c. 0.1141576 d. 0.511 e. 0.999999