A clothing company selected 1,000 persons at random and surveyed them to determine a relationship between the age of the purchaser and the annual purchases of jeans. The results are given in the table.

Given the events

A = person buys 2 pairs of jeans
B = person is between 12 and 18 years old
C = person does not buy more than 2 pairs of jeans
D = person buys more than 2 pairs of jeans

(A) Find P(A), P(B), P(A ∩ B), P(A |B), and P(B |A).

(B) Are events A and B independent? Explain.

(C) Find P(C), P(D), P(C ∩ D), P(C |D), and P(D |C).

(D) Are events C and D mutually exclusive? Independent? Explain.

Transcribed Image Text:

Jeans Purchased Annually 2 Age Above 2 Totals Under 12 60 70 30 10 170 12-18 30 100 100 60 290 19-25 70 110 120 30 330 Over 25 100 50 40 20 210 Totals 260 330 290 120 1,000