Question

stacy is choosing an entree and a dessert from a restaurant menu. let a be the event that she orders a sandwich for her entree. let b be the event that she orders something chocolate for dessert. stacys choice of dessert is independent of her choice of entree.
name two probabilities that must be equal.

1. the probability stacy orders a chocolate dessert
2. the probability stacy orders a sandwich or a chocolate dessert
3. the probability stacy orders a sandwich and a chocolate dessert
4. the probability stacy orders a sandwich and a chocolate dessert
5. the probability stacy orders a chocolate dessert if she has already ordered a sandwich
6. the probability stacy orders a sandwich if she has already ordered a chocolate dessert

Explanation:

Step1: Recall independence formula

For independent events $A$ and $B$, $P(B|A)=P(B)$.

Step2: Identify equal - probabilities

Since dessert choice is independent of entree choice, the probability Stacy orders a chocolate dessert is equal to the probability Stacy orders a chocolate dessert if she has already ordered a sandwich.

Answer:

The probability Stacy orders a chocolate dessert; the probability Stacy orders a chocolate dessert if she has already ordered a sandwich