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.

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2