Suppose PAi 13 i for i 1 2 3 4 Find an upper bound fir PA

Suppose P(A_i) = 1/(3 + i) for i = 1, 2, 3, 4. Find an upper bound fir P(A₁ Union A₂ Union A₃ Union A₄).

Solution

The probability of the union of mutually exclusive events in the sum of the probability of each event, as each event has probability (1/1 + i), \"i\" is being replaced by 1,2,3, and 4

P(A₁ U A₂ U A₃ U A₄) = (1/3+1) + (1/3+2) + (1/3+3) + (1/3+4) = (1/4) + (1/5) + (1/6) + (1/7) = 0.25 + 0.20 + 0.17 + 0.14

                                  = 0.76