Question

A group of people were asked what condiments they use on their hot dogs. They were asked whether they use ketchup, mustard, both ketchup and mustard, or neither ketchup nor mustard. Let A represent using ketchup and B represent using mustard. Which statement is true?

A) Using ketchup and using mustard are independent events because P(A|B) = P(A) and P(B|A) = P(B).
B) Using ketchup and using mustard are not independent events because P(A|B) = P(A) and P(B|A) = P(B).
C) Using ketchup and using mustard are independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
D) Using ketchup and using mustard are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

Answer 1

The correct answer is A) Using ketchup and using mustard are independent events because P(A|B) = P(A) and P(B|A) = P(B), signifying true independence of the two events.

Step-by-step explanation:

The question is asking about the independence of two events, A (using ketchup) and B (using mustard) on hot dogs. To determine if A and B are independent, we look at whether the probability of A happening given B has occurred, represented as P(A|B), is the same as the probability of A happening at any time, P(A), and vice versa for B. True independence is achieved when P(A|B) = P(A) and P(B|A) = P(B), and also if P(A AND B) = P(A)P(B).

With that in mind, the correct statement is: A) Using ketchup and using mustard are independent events because P(A|B) = P(A) and P(B|A) = P(B). This is because if two events are independent, knowing one occurred does not change the probability of the other occurring.