Chapter 12.8, Problem 41PPE

To determine

To find: The probability that all three acres will be farmland, find whether the choice of an acre from one state affect the choice from the other states, and write the method to write the percent to find the probability.

Answer to Problem 41PPE

The probability that all acres chosen are farmland is $\frac{9477}{200000}$ , choosing an acre of land from one state does not affect the choosing an acre of land from the other two states, and write the percents as fraction to find the probability.

Explanation of Solution

Given:

The given table is as follows.

Percent of State that is Farmland
Alabama	$27\%$
Florida	$27\%$
Indiana	$65\%$

Calculation:

The events are independent because choosing an acre of land from one state does not affect the choosing an acre of land from the other two states.

Write the percents as fraction which will be their probabilities.

  $\begin{array}{c}\text{Alabama}=\frac{27}{100}\\ \text{Florida}=\frac{27}{100}\\ \text{Indiana}=\frac{65}{100}\end{array}$

Find the probability that all acres chosen are farmland as follows.

  $\begin{array}{c}P\left(\text{all}\text{farmland}\right)=\frac{27}{100}\times \frac{27}{100}\times \frac{65}{100}\\ =\frac{9477}{200000}\end{array}$

Therefore, the probability that all acres chosen are farmland is $\frac{9477}{200000}$ , choosing an acre of land from one state does not affect the choosing an acre of land from the other two states, and write the percents as fraction to find the probability.