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 given that the other has occurred must equal the probability of the first event overall. The overall probability of grabbing shower gel is 42%, so independence requires P(shower gel | scented) = 42%. Choice C states this condition.
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