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?\no (p(\text{lotion}) = 42%)\no (p(\text{scented}) = 42%)\no (p(\text{shower gel}|\text{scented}) = 42%)\no (p(\text{scented}|\text{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?\no (p(\text{lotion}) = 42%)\no (p(\text{scented}) = 42%)\no (p(\text{shower gel}|\text{scented}) = 42%)\no (p(\text{scented}|\text{shower gel}) = 42%)

Answer

Explanation:

Step1: Recall independence formula

Two events $A$ and $B$ are independent if $P(A|B)=P(A)$. Let event $A$ be "shower - gel" and event $B$ be "scented". Given $P(\text{shower gel}) = 42%$. For "shower gel" and "scented" to be independent, the probability of getting a shower - gel given that it is scented should be equal to the probability of getting a shower - gel. That is $P(\text{shower gel}|\text{scented})=P(\text{shower gel}) = 42%$.

Answer:

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