Chapter 12.7, Problem 45PPE

To determine

To find: The probability that it will not be in the blue region if a point is randomly chosen inside the given figure.

Answer to Problem 45PPE

The probability that the point will not be in the blue region is $\frac{5}{8}$ .

Explanation of Solution

Given:

The given figure is as follows.

Calculation:

From the figure find the area of each region as follows.

  $\begin{array}{c}\text{White}\text{area}=4\text{sq}\text{unit}\\ \text{Red}\text{area}=3\text{sq}\text{unit}\\ \text{Blue}\text{area}=6\text{sq}\text{unit}\\ \text{Green}\text{area}=3\text{sq}\text{unit}\end{array}$

The total area is $16$ square units.

If the point is not in the blue region then it must be in other regions (white, red, and green).

Find the probability that the point will be in the blue region.

  $\begin{array}{c}\text{P}\left(\text{ event}\right)=\frac{\text{number}\text{of}\text{favorable}\text{outcomes}}{\text{number}\text{of}\text{possible}\text{outcomes}}\\ \text{P}\left(\text{not}\text{blue}\right)=\frac{4+3+3}{16}\\ =\frac{10}{16}\\ =\frac{5}{8}\end{array}$ .

Therefore, the probability that the point will not be in the blue region is $\frac{5}{8}$ .