§10.6, Geometric Probability

§10.6, Geometric Probability

Learning TargetsI will calculate geometric probabilities.

I will use geometric probability to predict results in real-world situations.

Vocabulary

geometric probability

Remember that in probability, the set of 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 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 experiment may be points on a segment or in a plane figure.

10-6

10-6

A point is chosen randomly on PS. Find the probability of each event.

The point is on RS. The point is on QS.

25

18

PS

QSP

The point is not on QR. The point is not on RS.

25

7

25

1811

PS

QSP

10-6

Use the figure below to find the probability that the point is on BD.

10-6

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

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.

The signal is “WALK” for 45 out of every 115 seconds.

0 45 115

45 70

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.

B

70

115

300

C023

6

115

30P

10-6

A traffic light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. When you arrive at the light was is the probability that it is green?

12

5

60

25)( greenP

10-6

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

The angle measure in the yellow region is 140°.

the pointer landing on blue or red

the pointer not landing on green

10-6

Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth.

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.

10-6

the trapezoid

The area of the rectangle is A = bh = 50(28) = 1400 ft2.

The area of the trapezoid is

The probability is

10-6

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

10-6

EXIT CHECK

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

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

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

0.25

EXIT CHECK

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

0.5

HOMEWORK:

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