juanita has a storage closet at her shop with extra bottles of lotion and shower gel. some are scented and…

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?\np(lotion) = 42%\np(scented) = 42%\np(shower gel | scented) = 42%\np(scented | shower gel) = 42%

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?\np(lotion) = 42%\np(scented) = 42%\np(shower gel | scented) = 42%\np(scented | shower gel) = 42%

Answer

Brief Explanations:

Two events A and B are independent if the conditional - probability of A given B is equal to the probability of A, i.e., (P(A|B)=P(A)). Here, event A is "shower gel" and event B is "scented". Given (P(\text{shower gel}) = 42%). For "shower gel" and "scented" to be independent, (P(\text{shower gel}|\text{scented})) must equal (P(\text{shower gel})), which is (42%).

Answer:

C. (P(\text{shower gel}|\text{scented}) = 42%)