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*Holt McDougal Geometry Geometric Probability Holt Geometry Warm Up Warm Up Lesson Presentation...*

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Slide 11.

2.

3.

3 points in the figure are chosen randomly. What is the probability that they are collinear?

0.2

Objectives

all possible outcomes of an experiment

is called the sample space. Any set of

outcomes is called an event.

If every outcome in the sample space is

equally likely, the theoretical probability

of an event is

Geometric 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 an

*

Geometric Probability

If an event has a probability p of occurring, the probability of the event not occurring is 1 – p.

Remember!

Geometric 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.

*

The point is not on QR.

*

The point is on PQ or QR.

P(PQ or QR) = P(PQ) + P(QR)

*

Check It Out! Example 1

*

Geometric Probability

A pedestrian signal at a crosswalk has the following cycle: “WALK” for 45 seconds and “DON’T WALK” for 70 seconds.

Example 2A: Transportation Application

What is the probability the signal will show “WALK” when you arrive?

To find the probability, draw a segment to represent the number of seconds that each signal is on.

*

Example 2B: Transportation Application

If you arrive at the signal 40 times, predict about how many times you will have to stop and wait more than 40 seconds.

In the model, the event of stopping and waiting

more than 40 seconds is represented by a segment that starts at B and ends 40 units from C. The probability of stopping and waiting more than 40

seconds is

If you arrive at the light 40 times, you will probably stop and wait more than 40 seconds about

(40) ≈ 10 times.

Check It Out! Example 2

Use the information below. What is the probability that the light will not be on red when you arrive?

*

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°.

*

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°.

*

the pointer not landing on green

The angle measure in the green region is 108°.

Subtract this angle measure from 360°.

*

Check It Out! Example 3

Use the spinner below to find the probability of the pointer landing on red or yellow.

*

Geometric 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

*

the circle

= (9)2 = 81 ≈ 254.5 ft2.

= 50(28) = 1400 ft2.

the trapezoid

= 50(28) = 1400 ft2.

The probability is

one of the two squares

The area of the two squares is A = 2s2

= 2(10)2 = 200 ft2.

= 50(28) = 1400 ft2.

The probability is

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.

*

Lesson Quiz: Part I

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.

3

5

13

15

Lesson Quiz: Part II

3. An antivirus program has the following cycle: scan: 15 min, display results: 5 min, sleep: 40 min. Find the probability that the program will be scanning when you arrive at the computer.

0.25

4. Use the spinner to find the probability of the pointer landing on a shaded area.

0.5

Lesson Quiz: Part III

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

0.25

2.

3.

3 points in the figure are chosen randomly. What is the probability that they are collinear?

0.2

Objectives

all possible outcomes of an experiment

is called the sample space. Any set of

outcomes is called an event.

If every outcome in the sample space is

equally likely, the theoretical probability

of an event is

Geometric 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 an

*

Geometric Probability

If an event has a probability p of occurring, the probability of the event not occurring is 1 – p.

Remember!

Geometric 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.

*

The point is not on QR.

*

The point is on PQ or QR.

P(PQ or QR) = P(PQ) + P(QR)

*

Check It Out! Example 1

*

Geometric Probability

A pedestrian signal at a crosswalk has the following cycle: “WALK” for 45 seconds and “DON’T WALK” for 70 seconds.

Example 2A: Transportation Application

What is the probability the signal will show “WALK” when you arrive?

To find the probability, draw a segment to represent the number of seconds that each signal is on.

*

Example 2B: Transportation Application

If you arrive at the signal 40 times, predict about how many times you will have to stop and wait more than 40 seconds.

In the model, the event of stopping and waiting

more than 40 seconds is represented by a segment that starts at B and ends 40 units from C. The probability of stopping and waiting more than 40

seconds is

If you arrive at the light 40 times, you will probably stop and wait more than 40 seconds about

(40) ≈ 10 times.

Check It Out! Example 2

Use the information below. What is the probability that the light will not be on red when you arrive?

*

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°.

*

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°.

*

the pointer not landing on green

The angle measure in the green region is 108°.

Subtract this angle measure from 360°.

*

Check It Out! Example 3

Use the spinner below to find the probability of the pointer landing on red or yellow.

*

Geometric 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

*

the circle

= (9)2 = 81 ≈ 254.5 ft2.

= 50(28) = 1400 ft2.

the trapezoid

= 50(28) = 1400 ft2.

The probability is

one of the two squares

The area of the two squares is A = 2s2

= 2(10)2 = 200 ft2.

= 50(28) = 1400 ft2.

The probability is

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.

*

Lesson Quiz: Part I

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.

3

5

13

15

Lesson Quiz: Part II

3. An antivirus program has the following cycle: scan: 15 min, display results: 5 min, sleep: 40 min. Find the probability that the program will be scanning when you arrive at the computer.

0.25

4. Use the spinner to find the probability of the pointer landing on a shaded area.

0.5

Lesson Quiz: Part III

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

0.25