at a store, the probability that a customer buys socks is 0.15. the probability that a customer buys socks given that the customer buys shoes is 0.20
Accepted Solution
A:
Answer: Option BStep-by-step explanation:First we assign a name to the events:Event S: a customer buys socksEvent 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