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)=0.15
The probability that a customer socks given that the customer buys shoes P(A\B)=0.20
The probability that a customer buys shoes,P(B)=1-0.15=0.85
By using formula P(E')=1-P(E)
Where P(E)= Probability of an event that is happened
P(E')=Probability of an event that is not happened
We 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.
Answer:
(A) Buying socks and buying shoes are dependent events.
Step-by-step explanation:
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