A sample space contains six sample points and events A, B, and C, as shown in the Venn dia...

A sample space contains six sample points and events A, B, and C, as shown in the Venn diagram on page 144. The probabilities of the sample points are P(1) = .20, P(2) = .05, P(3) = .30, P(4) = .10, P(5) = .10, and P(6) = .25.

a.  Which pairs of events, if any, are mutually exclusive? Why?

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b. Which pairs of events, if any, are independen Why?

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c.  Find P(A ⋃ B) by adding the probabilities of the sample points and then by using the additive rule. Verify that the answers agree. Repeat for P(A ⋃ C).