Chapter 12.7, Problem 35PPE

To determine

To find: The probability that the location in the United States is chosen at random is not in Illinois. Also, determine the method for the solution can be solved by the problem using the complement of the event and to write the fraction as the percent.

Answer to Problem 35PPE

The probability that the property is not in Illinois is $\frac{3478360}{3536278}$ or $0.9836$ and the probability percent that the location is chosen at random in United States and not in Illinois is $98.4\%$ .

Explanation of Solution

Given:

The land area of the United States $3,536,278{\text{mi}}^2$ and the land area is of about $\text{57,198}{\text{mi}}^2$ .

Calculation:

Consider the formula for the probability of the event is of the form,

  $P=\frac{\text{number}\text{of}\text{favorable}\text{outcomes}}{\text{number}\text{of}\text{possible}\text{outcomes}}$

Then, the probability that the property is not in Illinois is,

  $\begin{array}{c}P=1-P\left(\text{illinois}\right)\\ =1-\frac{57918}{3536278}\\ =\frac{3478360}{3536278}\\ =0.9836\end{array}$

The change in value in percent is $0.9836\times 100=98.36\%$ . This shows that location is chosen at random in United States and not in Illinois is $98.4\%$ .