The prior probabilities for events A1 and A2 are P (A1) = 0.20 and P (A2) = 0.50. It is also known that P (A1 ∩ A2) = 0. Suppose P (B | A1) = 0.20 and P (B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive?

Question

Mathematics

Oswaldo

12 August, 01:54

The prior probabilities for events A1 and A2 are P (A1) = 0.20 and P (A2) = 0.50. It is also known that P (A1 ∩ A2) = 0. Suppose P (B | A1) = 0.20 and P (B | A2) = 0.05. If needed, round your answers to three decimal digits. (a) Are A1 and A2 mutually exclusive?

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Edwin Collins · Answer 1

The inclusion-exclusion principle says

P (A1 ∩ A2) = P (A1) + P (A2) - P (A1 ∪ A2)

We know the probability of intersection is 0, so

P (A1) + P (A2) = P (A1 ∪ A2)

which means A1 and A2 are indeed mutually exclusive.