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?

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

Step-by-step 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.

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)