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E1 and E2 are events in a probability space satisfying the following constraints p(E1)= p(E2);p(E1U E2) = 1; E1 & E2 are independent then p(E1)=

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Given P(E1 U E2) = 1, P(E1) = P(E2), P(E1 intersection E2) = P(E2) * P(E2) (since E1 & E2 are independent).

Now by using inclusion exclusion principle, P(E1 U E2) = P(E1) + P(E2) - P(E1 intersection E2).

Let P(E1) = a, then P(E2) = a, and P(E1 intersection E2) = a * a. Putting all these values along with P(E1 U E2) = 1, leads to a quadratic equation a^2 - 2a + 1.

This equation gives a = P(E1) = P(E2) = 1.
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I think p(E1) =p(E2) =1

as they are independent and exhaustive .

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