11.5 Geometric probability

By: Ryan Jacob and Brinley Mathew

Objectives

• Solve problems involving Geometric Probability

• Solve problems involving sectors and segments of circles

Geometric Probability- Probability that involves a geometric measure such as length or area

In games, such as darts, you can use geometric probability to determine chances of winning

A

B

If a point in region A is chosen at random, then the probability P(B) that the point is in the region B, which is in the interior of region A, is

Example 1:

A dart is thrown at a square, black, and white dart board. What is the probability that the dart will hit a black square?

First we must count the number of square units in the box.

Then figure out how many black square units there are.

Then you set up a fraction of

(there are 36 square units altogether)

(there are 21 black square units)

Answer:

The sector of a circle is a region of a circle bounded by a central angle and its intercepted arc.

If a sector of a circle has an area of A square units, a central angle measuring N°, and a radius of r units,

a. Find the area of the red sector

10

^Don’t trust the picture

To find the red region use the formula

10

Area of sector

N= 69, r=5

= 4.8

b. Find the probability that a point chosen at random lies in the red region

To find the probability you use

=

~ ~.19

Segment- The region of a circle bounded by an arc and a chord.

To find the area of segment, subtract the area of the triangle formed by the radii and chord, from the area of the sector containing the segment.

Use this formula to find the probability of a segment.

=

a. Find area of the blue segment.

=

50.87

9

60°

30°9

Since the pentagon was inscribed, the 5 triangles formed are equilateral. To find the area of the triangle we must use 30-60-90 property to find the apothem (height)

RECAP -½ (Apothem x Perimeter) = Area of triangle

30°

60°

9

9

a

Find the apothem

Apothem= 4.5√3

7.8

Next find the area of the triangle

½ (7.8)(9)

Area of triangle 35.1 square units

Next, find the area of the segment by subtracting the area of the triangle from the area of the sector that holds the triangle

50.87- 35.1

= 15.77 square units

(blue area is the segment)

Answer: 15.77

b. Now find the probability that a point chosen lies in the blue region.

To do this you must use the formula -

=

Answer: .06 or 6%

.06 or 6%

Pre-AP Geometry: #7 odds only

APRIL FOOLS ON APRIL 7TH HAHHAHAHAHAHAHHA.

Real Pre-AP Geometry Assignment: 7-23 ALL