SOLUTION: Suppose P(Ai) = 1/(3 + i) for ¡ = 1, 2, 3, 4. Find an upper bound for P(A1 u A2 u A3 u A4)

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Question 1203571: Suppose P(Ai) = 1/(3 + i) for ¡ = 1, 2, 3, 4. Find an upper bound for P(A1 u A2 u A3 u A4)
Answer by ikleyn(52814) About Me  (Show Source):
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Suppose P(Ai) = 1/(3 + i) for ¡ = 1, 2, 3, 4. Find an upper bound for P(A1 u A2 u A3 u A4)
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We are given P(A1) = 1%2F4,  P(A2) = 1%2F5,  P(A3) = 1%2F6,  P(A4) = 1%2F7, according to the formula.


The problem asks to find the upper bound for P(A1 U A2 U A3 U A4).


It is obvious that the value  P(A1 U A2 U A3 U A4)  is maximum when all events A1, A2, A3, A4 are disjoint
(= are mutually exclusive). Then

    P(A1 U A2 U A3 U A4) = 1%2F4 + 1%2F5 + 1%2F6 + 1%2F7 = 105%2F420+%2B+84%2F420+%2B+70%2F420+%2B+60%2F420 = 319%2F420.


ANSWER.  The upper bound is 319%2F420.

Solved.