At a store, the probability that a customer buys socks is 0.15. The probabilitythat a customer buys socks given that the customer buys shoes is 0.20.Which statement is true?OA. Buying socks and buying shoes are dependent events.OB. The probability that a customer buys socks and shoes is 0.05.C. Every customer who buys shoes also buys socks.D. Buying socks and buying shoes are independent events.

Answer:A. Buying socks and buying shoes are dependent events.Step-by-step explanation:We are given that The probability that a customer buys socks ,P(A)=0.15The probability that a customer socks given that the customer buys shoes P(A\B)=0.20The probability that a customer buys shoes,P(B)=1-0.15=0.85By using formula P(E')=1-P(E)Where P(E)= Probability of an event that is happenedP(E')=Probability of an event that is not happenedWe have to find [tex]P(A\capB)[/tex]  for two events [tex]P(A)\cdot P(B)[/tex][tex]=0.85\times 0.15=0.1275[/tex]We know that conditional probability of an event when given that the probability of an event B is given [tex]P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)}[/tex][tex] 0.20=\frac{P(A\cap B)}{0.85}[/tex][tex]P(A\cap B)=0.20\times 0.85=0.17[/tex][tex]P(A\cap B)\neq P(A)\cdot P(B)[/tex].Therefore, the two events are dependent .Hence, Buying socks and buying shoes are dependent events.Therefore, option A is true.