7.9 Conditional Probability and the Multiplication Rule

1. April is playing a coin-flipping game with Ben. She will flip a coin 3 times. If the coin lands on heads more than tails, April wins; if it lands on tails more than heads, Ben wins. Let $A$ be the event “April wins,” $H$ be “first flip is heads,” and $T$ be “first flip is tails.” Compute $P \left(A\right)$, $P \left(\right. A \left|\right. H \left.\right)$, and $P \left(\right. A \left|\right. T \left.\right)$.
2. You are about to draw 2 cards without replacement from a deck containing only these 10 cards: $\text{A} ♡$, $\text{A} ♠$, $\text{A} ♣$,

You are president of a club with 10 members: 4 seniors, 3 juniors, 2 sophomores, and 1 first-year. You need to choose 2 members to represent the club on 2 college committees. The first person selected will be on the Club Awards Committee and the second will be on the New Club Orientation Committee. The same person cannot be selected for both. You decide to select these representatives at random.

1. …