if A, B, C are 3 equally likely events, what is the smallest value for P(A) such that P ( A ∩ B ∩ C ) always exceeds 0.95?
(use DeMorgan's Laws)
To find the smallest value of is equivalent to finding the largest value of .
Now the union of these three equal sets is largest when they are all disjoint (This can be proven formally using .)
Hence, the largest value of is , and it follows that the smallest value of is .