Chapter 8.4, Problem 33E

Pecans Pecan producers blow air through the pecans so that the lighter ones are blown out, The lighter-weight pecans are generally bad and the heavier ones tend to be better. These “blow outs” and “good nuts” are often sold to tourists along the highway. Suppose 60% of the “blow outs” are good, and 80% of the “good nuts” are good. Source: Irvin R. Hentzel.

(a) What is the probability that if you crack and check 20 “good nuts” you will find 8 bad ones?

(b) What is the probability that if you crack and check 20 “blow outs” you will find 8 bad ones?

(c) If we assume that 70% of the roadside stands sell “good nuts,” and that out of 20 nuts we find 8 that are bad, what is the probability that the nuts are “blow outs”?