Chapter 8, Problem 69RE

Market analysis. 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 $P\left(A\right),P\left(B\right),P\left(A\cap B\right),P\left(A\left|B\right.\right)\text{ and }P\left(B\left|A\right.\right)$.

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

(C) Find $P\left(C\right),P\left(D\right),P\left(C\cap D\right)\text{ and }P\left(D\left|C\right.\right).$

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