Solve problems involving geometric probability. Solve problems involving sectors and segments of...
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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