Solve the problem.
-A and B are events in a sample space S such that P(A) = 0.54, P(B) = 0.44, and P(A and B) = 0.14. Draw a Venn diagram showing the overlapping sets A and B and fill in the probabilities of the four regions formed.
A) x = 0.4, y = 0.14, z = 0.3, w = 0.16
B) x = 0.4, y = 0.14, z = 0.3, w = 0.02
C) x = 0.54, y = 0.14, z = 0.44, w = 0.12
D) x = 0.54, y = 0, z = 0.44, w = 0.02

Question

Quizplus · Accepted Answer

The probabilities of the regions in the Venn diagram are calculated as follows: $x = P(A) - P(A \text{ and } B) = 0.54 - 0.14 = 0.4$, $y = P(A \text{ and } B) = 0.14$, $z = P(B) - P(A \text{ and } B) = 0.44 - 0.14 = 0.3$, and $w = 1 - P(A \text{ or } B) = 1 - (P(A) + P(B) - P(A \text{ and } B)) = 1 - (0.54 + 0.44 - 0.14) = 0.16$.

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