A and B are events with P(A) = 0.5, P(B) = 0.4 and P(A⋂B) = 0.3. Find the probability that neither A and B occurs.

Engineering

Mathematics

Conditional Probability

Question

A and B are events with P(A) = 0.5, P(B) = 0 $.4$ and P(A⋂B) = 0.3. Find the probability that neither A and B occurs.

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P(A) = 0.5, P(B) = 0 $.4$ P(A⋂B) = 0.3.

P(AUB) = P(A) + P(B) – P(A⋂B)

= 0.5 = 0.4 – 0.3 = 0.6

Neither A nor B occurs

∴ P(A

⋂B

) c = 1 - P(AUB)

= 1 - 0.6 = 0.4

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