stacy is choosing an entree and a dessert from a restaurant menu. let a be the event that she orders a…

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. choose two probabilities that must be equal. a. the probability stacy orders a chocolate dessert b. the probability stacy orders a sandwich or a chocolate dessert c. the probability stacy orders a sandwich and a chocolate dessert d. the probability stacy orders a chocolate dessert if she has already ordered a sandwich e. the probability stacy orders a sandwich if she has already ordered a chocolate dessert

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. choose two probabilities that must be equal. a. the probability stacy orders a chocolate dessert b. the probability stacy orders a sandwich or a chocolate dessert c. the probability stacy orders a sandwich and a chocolate dessert d. the probability stacy orders a chocolate dessert if she has already ordered a sandwich e. the probability stacy orders a sandwich if she has already ordered a chocolate dessert

Answer

Explanation:

Step1: Recall the definition of independent events

If two events (A) and (B) are independent, then (P(B|A)=P(B)) and (P(A|B) = P(A)). Here, event (A) is ordering a sandwich for entree and event (B) is ordering a chocolate - dessert. Since the choice of dessert is independent of the choice of entree, the probability of ordering a chocolate dessert does not depend on whether or not a sandwich is ordered for the entree.

Step2: Analyze each option

  • Option A: The probability Stacy orders a chocolate dessert is (P(B)).
  • Option B: The probability Stacy orders a sandwich or a chocolate dessert is (P(A\cup B)=P(A)+P(B)-P(A\cap B)).
  • Option C: The probability Stacy orders a sandwich and a chocolate dessert is (P(A\cap B)=P(A)\times P(B)) (by independence).
  • Option D: The probability Stacy orders a chocolate dessert if she has already ordered a sandwich is (P(B|A)). Since (A) and (B) are independent, (P(B|A) = P(B)) (by the formula (P(B|A)=\frac{P(A\cap B)}{P(A)}) and (P(A\cap B)=P(A)P(B)) for independent events).
  • Option E: The probability Stacy orders a sandwich if she has already ordered a chocolate dessert is (P(A|B)), and (P(A|B)=P(A)) for independent events.

Answer:

A. the probability Stacy orders a chocolate dessert, D. the probability Stacy orders a chocolate dessert if she has already ordered a sandwich