Question

A point in the figure is chosen at random. Find the probability, as a percent (to the nearest tenth), that the point lies in the shaded region.

Answer 1

Step-by-step explanation

To find the probability that the point chosen lies in the shaded region, we will use the approach

Probability is simply the ratio of the number of possible outcomes to the total number of outcomes

In our case

The number of possible outcomes is the area of the shaded region

The total number of outcomes is the area of the rectangle

we will have the area of the rectangle as

`Area=length* breadth=length*2* radius=22*2*7=308m^2`

Next, we will get the area of the shaded region

This will be the difference between the area of the rectangle and that of the circle

`area\text{ of circle =}\pi r^2=\pi*7^2=153.94m^2`

Therefore, the area of the shaded region is

`308m^2-153.94m^2=154.06m^2`

Finally, the probability will be

`\frac{area\text{ of shaded region}}{area\text{ of rectangle}}=(154.06m^2)/(308m^2)=0.5`

The probability is 0.5

If we are to give our answers in terms of percentage

we will have:

`0.5*100\text{\%=50\%}`

The probability that A point in the figure lies in the shaded region will be 50.0%