Problem 1: Given the following probabilities P (Ac) = 0.45, P (B) = 0.34, and P (B|A) = 0.23. Find the following probabilities:

P (A)

P (A and B)

P (A or B)

P (A|B)

P (A) = 0.55

P (A and B) = P (A∩B) = 0.1265

P (A or B) = P (A∪B) = 0.7635

P (A|B) = 0.3721

Step-by-step explanation:

P (A') = 0.45

P (A) = 1-0.45=0.55

P (B∩A) = ?

P (B|A) = 0.23

P (B|A) = (P (A∩B)) / P (A)

0.23 = (P (A∩B)) / 0.55

P (A∩B) = 0.23*0.55=0.1265

P (A∪B) = P (A) + P (B) - P (A∩B)

=0.55+0.34-0.1265

=0.7635

P (A|B) = [P (A∩B) ]/P (B) = 0.1265/0.34 ≈0.3721