The geometric probability of an event is a ratio that involves geometric measures such as length or area. Compare the part that represents favorable outcomes to the whole, which represents all outcomes.
3/8, 0.375, or 37.5 %
Practice makes perfect
We can use geometric models to solve certain types of probability problems. In geometric probability, points on a segment or 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 is chosen at random from the given figure in the shape of a square. We want to find the probability that the point lies in the shaded region, which is the ratio of the area of the shaded region to the area of the figure.
P(The point lies in the shaded region)= [0.8em]
Area of the shaded region/Area of the figure
The given figure is divided into 16 congruent squares. To find the ratio between the shaded region and the whole region, let's count how many out of these 16 squares are shaded.
Six parts are shaded. Therefore, the area of the shaded region is equal to 6, and the area of the figure is equal to 16. Now that we know both areas, we can find their ratio.
