Question

At the mall, buying a pair of shoes and buying a book are independent events.The probability that a shopper buys shoes is 0.12. The probability that ashopper buys a book is 0.10.What is the probability that a shopper buys shoes and a book?A. 0.12B. 0.02C. 0.22D. 0.012

Answer 1

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

`\begin{gathered} A:\text{ shopper buys shoes} \\ B:\text{ shopper buys a book} \end{gathered}`

They are independent, which means that

`A\cap B=\emptyset`

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

`P(A\cap B)=P(A)\cdot P(B)`

Hence we have that

`P(A\cap B)=0.12\cdot0.10`

Multiplying the numbers gives you

`P(A\cap B)=0.012`

This is the answer to this question and it is contained in the last option.