Question

Juanita has a storage closest at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closest and grabs a bottle without looking, she has 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 1

P(shower gel | scented) = 42%

Answer 2

The probability of choosing a shower gel given the item is scented must be the same as grabbing shower gel, or 42%.

Explanation:

To determine if two events are independent using their probabilities, we look for:

P(A|B) = P(A);

P(B|A) = P(B);

or P(A∩B) = P(A)·P(B)

We know that the probability she chooses a shower gel is 42%. Letting this be event A, we have:

P(shower gel | scented) = P(shower gel) = 42%

This must be true for the events to be independent.