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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: P1 + P2 – 2P1P2
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Solution
Here, P(E1) = P1 and P(E2) = P2
P1 + P2 – 2P1P2 = P(E1) + P(E2) – 2P(E1).P(E2)
= P(E1) + P(E2) – 2P(E1 ∩ E2)
= P(E1 ∪ E2) – 2P(E1 ∩ E2)
So, either E1 or E2 occurs but not both.
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