Respuesta :
Hello there. To solve this question, we have to remember some properties about probabilities.
Given that buying a pair of shoes and buying a book are independent events and the probability a shopper buys shoes is 0.12 and the probability that a shopper buys a book is 0.10, we want to determine:
The probability that a shopper buys shoes and a book.
For this, say that the events
[tex]\begin{gathered} A:\text{ shopper buys shoes} \\ B:\text{ shopper buys a book} \end{gathered}[/tex]They are independent, which means that
[tex]A\cap B=\emptyset[/tex]But we're looking for the probability of the shopper buying shoes and a book, therefore the probability of the intersection of events is not zero.
We use the conditional probability to prove that
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]Hence we have that
[tex]P(A\cap B)=0.12\cdot0.10[/tex]Multiplying the numbers gives you
[tex]P(A\cap B)=0.012[/tex]This is the answer to this question and it is contained in the last option.
