(Solved): e Venn diagram below shows the 9 students in Ms. Ramirez's class. The diagram shows the memberships ...

e Venn diagram below shows the 9 students in Ms. Ramirez's class. The diagram shows the memberships for the Tennis Club and the Soccer Club. A student from the class is randomly selected. Let $A$ denote the event "the student is in the Tennis Club." Let $B$ denote the event "the student is in the Soccer Club." The outcomes for the event $A$ are listed in the circle on the left. The outcomes for the event $B$ are listed in the circle on the right. Note that Rachel is outside the circles since she is not a member of either club. Answer each part below. If necessary, consult a list of formulas. (a) Find the probabilities of the events below. Write each answer as a single fraction. $\begin{array}{l}P(A)=\Vert \mathbb{I}\\ P(B)=\\ P(A\text{ and }B)=\\ P(B\mid A)=\\ P(A)\cdot P(B\mid A)=\end{array}$ (b) Select the probability that is equal to $P(A$ and $B)$. $\begin{array}{l}P(A)\cdot P(B\mid A)\\ P(B\mid A)\\ P(B)\\ P(A)\end{array}$