In these lessons, we will learn how to solve probability problems that may involve geometry and the area of geometrical shapes.

Related Topics: More Probability Lessons

Geometric Probability with Area

Example 1: A circle with radius 2 lies inside a square with side length 6. A dart lands randomly inside the square. What is the probability the dart lands inside the circle? Give the exact probability and the probability as a percent rounded to the nearest tenth.

Example 2: A point is chosen at random on the given figure. What is the probability that the point is in the yellow region?

Example 3: A square is inscribed in a circle. What is the probability that a point chosen inside the circle will be inside the square?

Example 4: A circle is inscribed in a equilateral triangle. What is the probability that a point chosen at random inside the triangle will be insode the circle?
Using Area to find Probability

Example: A circle is inscribed in a square. Point Q in the square is chosen at random. What is the probability that Q lies in the shaded region?

Geometric Probability and Areas of Sectors.
Study Guide Area Probability Problem 1.

Study Guide Area Probability Problem 2.
Geometric Probability.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Related Topics: More Probability Lessons

* Example: *

*ABCD * is a square. *M* is the midpoint of *BC* and *N *is the midpoint of *CD*. A point is selected at random in the square. Calculate the probability that it lies in the triangle *MCN*.

* Solution: *

Let 2*x* be the length of the square.

Area of square = 2*x* × 2*x* = 4*x*^{2}

* Example: *

The figure shows a circle with centre *O *and radius 8 cm. Ð* BOD* = 72˚. The radius of the smaller circle is 4 cm. A point is selected at random inside the larger circle *BCDE*.

Calculate the probability that the point lies

a) inside the sector *BODC*.

b) inside the smaller circle

c) neither in the sector *BODC* nor in the smaller circle.

* Solution: *

a)

Area of sector *BODC* = × area of the large circle

Probability that the point lies in sector *BODC* =

b)

Area of smaller circle = × area of the large circle

Probability that the point lies in the smaller circle =

c) Probability that the point does not lie in sector *BODC* or the smaller circle

Example 1: A circle with radius 2 lies inside a square with side length 6. A dart lands randomly inside the square. What is the probability the dart lands inside the circle? Give the exact probability and the probability as a percent rounded to the nearest tenth.

Example 2: A point is chosen at random on the given figure. What is the probability that the point is in the yellow region?

Example 3: A square is inscribed in a circle. What is the probability that a point chosen inside the circle will be inside the square?

Example 4: A circle is inscribed in a equilateral triangle. What is the probability that a point chosen at random inside the triangle will be insode the circle?

Example: A circle is inscribed in a square. Point Q in the square is chosen at random. What is the probability that Q lies in the shaded region?

Study Guide Area Probability Problem 2.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.