Question

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?

P(lotion) = 42%

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

Answer 1

i think its the third option

Answer 2

`she has a 42% chance of grabbing a bottle of shower gel.`
so the problem is stating P(shower gel) = 0.42 = 42%

Answer 3

If you can show that `P(shower gel | scented) = 42%` then you will have shown that the two events are independent

if `P(shower gel | scented)` is not equal to 42%, then that will show the "scented" event somehow alters the "shower gel" event, which would mean the two events would be dependent

Answer 4

so its not the third option? i understand what your saying

Answer 5

i think its the second option. because the lotion and body wash could be scented

Answer 6

the answer is P(shower gel | scented) = 42%

Answer 7

together you need to show that

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

for the two events to be independent

Answer 8

the first part is already given

Answer 9

oh okay I understand know. I was totally thrown off

Answer 10

thank you

Answer 11

yeah the problem isn't 100% straightforward

Answer 12

no problem