11.5 Geometric Probability

Objectives

Solve problems involving geometric probability.

Solve problems involving sectors and segments of circles.

Probability and Area

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

A

BP(B)=area of

region Barea of region A

Example 1

Suppose this is a dart board. You are trying to hit the red part of the board. Determine the probability that this will happen.

A = 81 units2

A = 25 units2

P(Red) =

2581

Probability with Sectors

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

=A

and recall… P(B) = area of sector area of circle

Nº

r

O

N360

(pr2

)

• Sector- a region of the circle bounded by its central

angle and its intercepted arc.

Example 2

57°46°

50°70°80°

57° 12

Find the area of the blue sector. Keep in terms of pi.

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

Segments of Circles

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

arc

chord

segment

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

N 360

(pr2) -

1∕2bh

Example 3

14

Find the area of the red segment. Assume that it is a regular hexagon.First find area of a sector.Then find the area of a triangle.Then subtract the area of the triangle from the area of the sector to find the area of the red segment.

What is the probability that a random point is in the red segment?

Assignment

GEOMETRY

Pg.625 #7-23, 26 - 28