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Find the best constant a

Give examples of events to show that these bounds cannot be improved (SEE ATTACHED).

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We know that P(AUB) = P(A) + P(B) - P(A intersection B)
Or P(AUB) = 1/2 + 1/3 - P(A intersection B)
Or P(AUB) = 5/6 - P(A intersection B)
But P(AUB) >= 1/2
Therefore, ...

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