Question 1203571
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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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<pre>
We are given P(A1) = {{{1/4}}},  P(A2) = {{{1/5}}},  P(A3) = {{{1/6}}},  P(A4) = {{{1/7}}}, 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) = {{{1/4}}} + {{{1/5}}} + {{{1/6}}} + {{{1/7}}} = {{{105/420 + 84/420 + 70/420 + 60/420}}} = {{{319/420}}}.


<U>ANSWER</U>.  The upper bound is {{{319/420}}}.
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Solved.