holt mcdougal geometry 10-6 geometric probability 10-6 geometric probability holt geometry warm up...
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Holt McDougal Geometry
10-6Geometric Probability10-6 Geometric Probability
Holt Geometry
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt McDougal Geometry
Holt McDougal Geometry
10-6Geometric Probability
Warm UpFind the area of each figure.
1. A = 36 ft2
A = 20 m22.
3.
A = 261 in2
10 in
Holt McDougal Geometry
10-6Geometric Probability
Calculate geometric probabilities.
Use geometric probability to predict results in real-world situations.
Objectives
Holt McDougal Geometry
10-6Geometric Probability
geometric probability
Vocabulary
Holt McDougal Geometry
10-6Geometric Probability
Remember that in probability, the set ofall possible outcomes of an experimentis called the sample space. Any set ofoutcomes is called an event.
If every outcome in the sample space isequally likely, the theoretical probabilityof an event is
Holt McDougal Geometry
10-6Geometric Probability
Geometric probability is used when an experiment has an infinite number of outcomes. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of anexperiment may be points on a segment or in a plane figure.
Holt McDougal Geometry
10-6Geometric Probability
Holt McDougal Geometry
10-6Geometric Probability
A point is chosen randomly on PS. Find the probability of each event.
Example 1A: Using Length to Find Geometric Probability
The point is on RS.
Holt McDougal Geometry
10-6Geometric Probability
Example 1B: Using Length to Find Geometric Probability
The point is not on QR.
Subtract from 1 to find the probability that the point is not on QR.
PQ + RS
PS=
7 + 5
25=
12
25
Holt McDougal Geometry
10-6Geometric Probability
Example 1C: Using Length to Find Geometric Probability
The point is on PQ or QR.
P(PQ or QR) = P(PQ) + P(QR)
Holt McDougal Geometry
10-6Geometric Probability
Check It Out! Example 1
Use the figure below to find the probability that the point is on BD.
Holt McDougal Geometry
10-6Geometric Probability
Use the spinner to find the probability of each event.
Example 3A: Using Angle Measures to Find Geometric Probability
the pointer landing on yellow
The angle measure in the yellow region is 140°.
Holt McDougal Geometry
10-6Geometric Probability
Example 3B: Using Angle Measures to Find Geometric Probability
the pointer landing on blue or red
The angle measure in the blue region is 52°.
The angle measure in the red region is 60°.
Use the spinner to find the probability of each event.
Holt McDougal Geometry
10-6Geometric Probability
Example 3C: Using Angle Measures to Find Geometric Probability
the pointer not landing on green
The angle measure in the green region is 108°.
Subtract this angle measure from 360°.
Use the spinner to find the probability of each event.
Holt McDougal Geometry
10-6Geometric Probability
Check It Out! Example 3
Use the spinner below to find the probability of the pointer landing on red or yellow.
The probability is that the
spinner will land on red or
yellow.
Holt McDougal Geometry
10-6Geometric Probability
Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth.
Example 4: Using Area to find Geometric Probability
Holt McDougal Geometry
10-6Geometric Probability
Example 4A: Using Area to find Geometric Probability
the circle
The area of the circle is A = r2
= (9)2 = 81 ≈ 254.5 ft2.
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The probability is P = 254.51400
≈ 0.18.
Holt McDougal Geometry
10-6Geometric Probability
the trapezoid
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The area of the trapezoid is
The probability is
Holt McDougal Geometry
10-6Geometric Probability
one of the two squares
The area of the two squares is A = 2s2
= 2(10)2 = 200 ft2.
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The probability is
Holt McDougal Geometry
10-6Geometric Probability
Check It Out! Example 4
Area of rectangle: 900 m2
Find the probability that a point chosen randomly inside the rectangle is not inside the triangle, circle, or trapezoid. Round to the nearest hundredth.
The probability of landing inside the triangle (and circle) and trapezoid is 0.29.Probability of not landing in these areas is 1 – 0.29 = 0.71.
Holt McDougal Geometry
10-6Geometric Probability
Review:
A point is chosen randomly on EH. Find the probability of each event.
1. The point is on EG.
2. The point is not on EF.
35
1315
Holt McDougal Geometry
10-6Geometric Probability
Review:
3. Use the spinner to find the probability of the pointer landing on a shaded area.
0.5
4. Find the probability that a point chosen randomly inside the rectangle is in the triangle.
0.25