Shade and calculate Venn regions, then apply conditional probability.

The following Venn diagram shows the universal set \(U\) and the sets \(A\) and \(B\).

1. Shade the area in the diagram which represents the set B ∩ A'. n(U) = 100, n(A) = 30, n(B) = 50, n(A ∪ B) = 65.
2. Find n(B ∩ \(A\prime\)).
3. An element is selected at random from U. What is the probability that this element is in B ∩ \(A\prime\) ?

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