Suppose A and B are two events of a sample space S where PA

Suppose A and B are two events of a sample space S where P(A) = 0.32, P(B) = 0.32, and P(A B) = 0.5. What is P(A B)? Are A and 8 independent events? Yes No If A and B are Independent events, P{A) = 0.35, and P(B) = 0.45, find the probabilities below. (Enter your answers to four decimal places.) P(A B) P(A B) P(A|B) P(A^C B^C)

Solution

P(AnB) = P(A) + P(B) - P(AuB)

P(AnB) = 0.32 + 0.32 - 0.5

P(AnB) = 0.14

A and B will be independent events if

P(AnB) = P(A)*P(B)

which is not true, so A and B are not independent events.

2.

A.

P(AnB) = P(A)*P(B)

P(AnB) = 0.35*0.45 = 0.1575

B.

P(AuB) = P(A) + P(B) - P(AnB)

P(AuB) = 0.35 + 0.45 - 0.1575 = 0.6425

C.

P(A|B) = P(A) = 0.35

D.

P(A\'UB\') = 1 - P(AuB)

= 1 - 0.6425 = 0.3575