We can use geometric models to solve certain types of probability problems. In geometric probability, points on a segment or in a region of a plane represent outcomes. The geometric probability of an event is a ratio that involves geometric measures such as length or area. Consider the given diagram.
We are told that a point in the figure is chosen at random, and want to find the probability that the point lies in the shaded region. The probability that the point is in the shaded region is the ratio of the area of the shaded region to the area of the figure.
P(The point is in the shaded region)= [0.8em]
Area of the shaded region/Area of the figure
We will find the area of the entire figure and the area of the shaded region one at a time. Then, we will find their ratio.
The area of the shaded region is the difference between the area of the figure and the area of a square with side length 3 meters. We already know that the area of the figure is 25 square meters. Let's calculate the are of the inner square.
Area of the Inner Square: 3^2= 9m^2
To find the area of the shaded region, we will subtract the area of the inner square from the area of the entire figure.
Shaded Area: 25 - 9= 16 m^2
Probability
As previously mentioned, the probability that the point is in the shaded region is the ratio of the area of the shaded region to the area of the figure. Since we already know both areas, we can find their ratio.
