Probability Lesson 3Geometric Probability and the Addition

Rule

The Standard

MCC9-12.S.CP.7 Apply the Addition Rule P{A or B)=P(A)+P(B)-P(A and B), and interpret the answer in terms of the model

Learning Target

I can use geometry or the addition rule to determine probabilities.

Vocabulary

Geometric probability- the probability of an event is based on a ratio of geometric measures such as length or area.

Models for geometric probability

There are three models for geometric probability:

LengthAngle measureArea

Geometric Probability: Length

.. 

XZ

XY

5

14

XYP

XZ

A point is chosen at random on

Find the probability that the point is on

length

Geometric Probability : Length

1.Look at the example for length. The probability that a point chosen

at random on XZ is on YZ can be

written as

YZP .

2. Write the probability described in Exercise 1 as a percent to the nearest whole percent. ______________________

Geometric Probability: Angle Measure

angle measure

Find the probability that the pointer does not land on white.

360 60 300 5

360 360 6P

Geometric Probability: Angle Measure

3. Look at the example for angle measure. What is the probability that the pointer DOES land on white? ______________________

4. How is your answer to Exercise 3 related to the answer in the example? Why?

angle measure

Find the probability that the pointer does not land on white.

360 60 300 5

360 360 6P

Geometric Probability: Area

area

Find the probability that a point chosen randomly inside the rectangle is in the square.

Area of the rectangle:

A bh 25(10) cm2 250 cm2

Area of the square: A s

2 (5)2 cm2 25 cm2

25 1

250 10P

Geometric Probability: Area

5. Look at the example for area. Find the probability that a point chosen randomly inside the rectangle is in the parallelogram. ______________________

area

Find the probability that a point chosen randomly inside the rectangle is in the square.

Area of the rectangle:

A bh 25(10) cm2 250 cm2

Area of the square: A s

2 (5)2 cm2 25 cm2

25 1

250 10P