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% 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 open paren scented divides shower gel close paren is equal to 42 percent
B
cap p times open paren shower gel divides scented close paren is equal to 42 percent
C
cap p times scented is equal to 42 percent
D
cap p times lotion is equal to 42 percent
Explanation
For two events to be independent, the probability of one event given the other must equal the probability of the first event. Here, P(shower gel) = 42%, so independence requires P(shower gel | scented) = 42%. Choice B states exactly this condition. Choice A instead gives the probability of scented given shower gel, which is not the condition asked for here.
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