(Solved): A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The ...

A sample space contains six sample points and events A, B, and C as shown in the Venn diagram. The probabilities of the sample points are \( P(1)=0.10, P(2)=0.15, P(3)=0.30, P(4)=0.05, P(5)=0.05 \), and \( P(6)=0.35 \). Complete parts a through \( \mathbf{c} \). Click the icon to see the Venn diagram. a. Which pairs of events, if any, are mutually exclusive? Why? Select all that apply. A. Events \( \mathrm{A} \) and \( \mathrm{C} \) are mutually exclusive because they do not have any sample points in common, B. Events \( A \) and \( B \) are mutually exclusive because they do not have any sample points in common. C. Events \( A \) and \( B \) are mutually exclusive because they share at least one sample point. D. Events \( \mathrm{A} \) and \( \mathrm{C} \) are mutually exclusive because they share at least one sample point. E. Events \( \mathrm{B} \) and \( \mathrm{C} \) are mutually exclusive because they do not have any sample points in common. F. Events \( \mathrm{B} \) and \( \mathrm{C} \) are mutually exclusive because they share at least one sample point. G. There are no mutually exclusive pairs of events. Venn Diagram