Me with these two statistic questions.

1. a lot of 953 components contains 379 that are defective. two components are drawn at random and tested. let a be the event that the first component drawn is defective, and let b be the event that the second component drawn is defective. write your answer as a fraction or a decimal, rounded to four decimal places.

find the solutions for a, b, c, and d.
(a) find p(a)

(b) find p(b and a.)

(c) find p(a and b).

(d) are a and b independent? is it reasonable to treat a and b as though they were independent? explain.

2. quality control: a population of 597 semiconductor wafers contains wafers from three lots. the wafers are categorized by lot and by whether they conform to a thickness specification, with the results shown in the following table. a wafer is chosen at random from the population. write your answer as a fraction or a decimal, rounded to four decimal places.

lot conforming nonconforming
a 80 12
b 157 46
c 268 34

(a) what is the probability that the wafer is from lot b?

(b) what is the probability that the wafer is conforming?

(c) what is the probability that the wafer is from lot b and is conforming?

(d) given that the wafer is from lot b, what is the probability that it is conforming?

(e) given that the wafer is conforming, what is the probability that it is from lot b?

(f) let e1 be the event that the wafer comes from lot b, and let e2 be the event that the wafer is conforming. are e1 and e2 independent?

you!