Answer: Option B
Step-by-step explanation:
First we assign a name to the events:
Event S: a customer buys socks
Event H: a customer buys shoes.
We know that :
[tex]P (S) = 0.15[/tex]
We also know that the probability of S given that H occurs is:
[tex]P(S|H) =\frac{P(S\ and\ H)}{P(H)}=0.20[/tex]
If two events S and H are independent then:
[tex]P (S) * P (H) = P (S\ and\ H)[/tex]
This mean that if two events S and H are independent then:
[tex]P(S|H) =\frac{P(S)*P(H))}{P(H)}[/tex]
[tex]P(S|H) =P(S)[/tex]
We know that:
[tex]P(S|H) =0.20[/tex] and [tex]P (S) = 0.15[/tex]
[tex]0.20\neq 0.15[/tex]
This means that S and H events are dependent.
The answer is the option B
