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?

Answer 1

Answer:

For this case if the two events described are independent we need to satisfy:

1) $P(shower-gel | scented) =0.42$

Since by definition of independence the event shower gel is not dependent of the event scented

We also need to have that:

$P(scented |shower- gel) = P(scented)$

And the second condition that we need to satisfy is :

2) $P(shower-gel \cap scented) = P(shower-gel) *P(scented)$

The product of the individual probabilities represent the intersection of the two events

If we satisfy the conditions described above then we can consider the events "shower gel" and "scented" as independent events.

Step-by-step explanation:

For this case if the two events described are independent we need to satisfy:

1) $P(shower-gel | scented) =0.42$

Since by definition of independence the event shower gel is not dependent of the event scented

We also need to have that:

$P(scented |shower- gel) = P(scented)$

And the second condition that we need to satisfy is :

2) $P(shower-gel \cap scented) = P(shower-gel) *P(scented)$

The product of the individual probabilities represent the intersection of the two events

If we satisfy the conditions described above then we can consider the events "shower gel" and "scented" as independent events.

Answer 2

Answer:

P(shower gel | scented) = 42%

Step-by-step explanation:

Was right on edge