Question 13 • Concepts in Probability and Statistics
Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42 percent chance of grabbing a bottle of shower gel. For the events "shower gel” and "scented” to be independent, what must be shown to be true?
Answer
A
cap p times lotion is equal to 42 percent
B
cap p times scented is equal to 42 percent
C
cap p times open paren scented divides shower gel close paren is equal to 42 percent
D
cap p times open paren shower gel divides scented close paren is equal to 42 percent
Explanation
For two events to be independent, the probability of one event occurring given that the other occurred must equal the first event’s overall probability. Here, the overall probability of shower gel is 42%, so independence requires P(shower gel | scented) = 42%. That is choice D, “P(shower gel given scented) is equal to 42 percent.”
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