91Ó°ÊÓ

Let \(\Omega\) consist of the set of positive integers. Consider the subsets $$A=\\{\omega: \omega \leq 12\\} \quad B=\\{\omega: \omega<8\\} \quad C=\\{\omega: \omega \text { is even }\\}$$ \(D=\\{\omega: \omega\) is a multiple of 3\(\\} \quad E=\\{\omega: \omega\) is a multiple of 4\(\\}\) Describe in terms of \(A, B, C, D, E\) and their complements the following sets: a. \\{1,3,5,7\\} b. \\{3,6,9\\} c. \\{8,10\\} d. The even integers greater than 12 . e. The positive integers which are multiples of six. f. The integers which are even and no greater than 6 or which are odd and greater than 12 .

A committee of five is chosen from a group of 20 people. What is the probability that a specified member of the group will be on the committee?

Suppose \(P(A)=0.5\) and \(P(B)=0.3 .\) What is the largest possible value of \(P(A B) ?\) Using the maximum value of \(P(A B),\) determine \(P\left(A B^{c}\right), P\left(A^{c} B\right), P\left(A^{c} B^{c}\right)\) and \(P(A \cup B)\). Are these values determined uniquely?

Determine the probability \(P(A \cup B \cup C)\) in terms of the probabilities of the events \(A, B, C\) and their intersections.