Marcus works as a waiter on the weekends and in the evenings after classes.7% of the time he gets a customer's food order wrong.3% of the time he gets a customer's drink order wrong.Two percent of the time, he gets both orders wrong.According to these numbers, are the two events-getting the drink order wrong and getting the food order wrong- statistically independent?
A)Yes, since P(wrong food given wrong drink) is equal to P(wrong food).
B)No, since P(wrong food given wrong drink) is not equal to P(wrong drink).
C)No, since P(wrong food given wrong drink) is not equal to P(wrong food).
D)Yes, P(wrong food given wrong drink) is equal to P(wrong drink).
E)Yes, P(wrong food given wrong drink) is equal to P(wrong food).

Question

Quizplus · Accepted Answer

Two events are statistically independent if the probability of one event occurring does not affect the probability of the other event. The formula to check for independence is P(A and B) = P(A) * P(B). Here, P(wrong food) = 7%, P(wrong drink) = 3%, and P(wrong food and wrong drink) = 2%. If the events were independent, P(wrong food and wrong drink) should equal P(wrong food) * P(wrong drink) = 0.07 * 0.03 = 0.0021 or 0.21%, which is not the case. Therefore, the events are not independent.

Marcus Works as a Waiter on the Weekends and in the Evenings