Question

Sophla runs a clothing store in a mall. Yesterday she counted that of the 121 who walked by thestore, 52 came into the store. Of the 52 who came in to the store, only 29 bought something.*Round all probablities to three decimal places**a) What is the probability that a person who walked by the store would come in to the store?b) What is the probability that a person who enters the store will buy something?c) What is the probability that a person who walks by the store will buy something?d) What is the probability that a person who comes into the store will buy nothing?

Answer 1

Let us begin by defining the formula for calculating probability of an event occuring:

`P(an\text{ event occuring) = }\frac{Number\text{ of times the event occured}}{Total\text{ number of trials}}`

Before we proceed, let us enumerate the given variables

121 people walked by the store

52 came into the store

29 bought something

(a) The probability that a person who walked by the store would come into the store:

`P\text{ = }\frac{Number\text{ who came into the store}}{Number\text{ that walked by}}`

Substituting we have:

`\begin{gathered} P\text{ = }(52)/(121) \\ \approx\text{ 0.430} \end{gathered}`

Answer: 0.430

(b) The probability that a person who enters the store will buy something

`P\text{ = }\frac{Number\text{ that bought something}}{Number\text{ who entered the store}}`

Substituting we have:

`\begin{gathered} P\text{ = }(29)/(52) \\ \approx\text{ 0.558} \end{gathered}`

Answer: 0.558

(c) The probability that a person who walks by the store will buy something

`P\text{ = }\frac{\text{Numb}er\text{ that bought something}}{Number\text{ that walked by}}`

Substituting we have:

`\begin{gathered} P\text{ = }(29)/(121) \\ \approx\text{ 0.240 } \end{gathered}`

Answer: 0.240

(d) The probability that a person who comes into the store will buy nothing

To calculate this, we use the formula:

`\begin{gathered} P(A)\text{ + P(A') =1} \\ \text{Where P(A') is the probability that an event would not occur} \end{gathered}`

The probability that a person who comes into the store would buy something is 0.558

Hence:

`\begin{gathered} P\text{ = 1 - 0.558} \\ =\text{ 0.442} \end{gathered}`

Answer: 0.442