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Question
Let E1 and E2 be two independent events such that P(E1) = P1 and P(E2) = P2. Describe in words of the events whose probabilities are: 1 – (1 – P1)(1 – P2)
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Solution
Here, P(E1) = P1 and P(E2) = P2
1 – (1 – P1)(1 – P2) = 1 – P(E1)'P(E2)'
= 1 – P(E1' ∩ E'2)
= 1 – [1 – P(E1 ∪ E2)]
= P(E1 ∪ E2)
So, either E1 or E2 or both E1 and E2 occur.
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