Suppose R and Q are two events such that P(R)= .14, P(Q) = .52, and P(R∩Q)= .20, find P(RUQ), are the events mutually exclusive why or why not?

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P(R I Q) = P(RnQ) / P(Q) = 0.1 Therefore P(RnQ) = 0.1 X 0.35 = 0.035 (The intersection in the centre of a Venn Diagram)

P(RnQ') = 0.15 In a Venn Diagram this is R but excluding the centre intersection with Q. Therefore P(R) = P(RnQ') + P(RnQ) = 0.15 + 0.035 = 0.185

P(RUQ) = 0.15 + 0.035 + 0.315 = 0.5 so 0.5 must be outside the Venn Diagram circles.

Explanation:

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