Geometric Probability

The student is able to (I can):

Calculate geometric probabilites

Use geometric probability to predict results in real-world situations

theoretical probability

geometric probability

If every outcome in a sample space is equally likely to occur, then the theoretical probability of an event is

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.

number of outcomes in the eventP

number of outcomes in the sample space=

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

1. The point is on .

2. The point is notnotnotnot on .

RD

DAER

4 3 5

RA

( ) = RAP RARD

7

12=

RE

( ) ( )P not RE 1 P RE= RE1RD

=

41

12=

8 2

12 3= =

Examples A stoplight has the following cycle: green for 25 seconds, yellow for 5 seconds, and red for 30 seconds.

1. What is the probability that the light will be yellow when you arrive?

( ) = 5P yellow60

1

12=

Examples

2. If you arrive at the light 50 times, predict about how many times you will have to wait more than 10 seconds.

Therefore, if you arrive at the light 50 times, you will probably stop and wait more than 10 seconds about

10E20

CEP

AD=

20

60=

1

3=

( )1 50 17 times3

Examples Use the spinner to find the probability of each event.

1. Landing on red

2. Landing on purple or blue

3. Not landing on yellow

80P

360=

2

9=

75 60P

360

+=

135

360=

3

8=

360 100P

360

=260

360=

13

18=

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

1. The circlecircle

Prectangle

=

( )( )( )

29

28 50

pi= 0.18

Examples

2. The trapezoid

trapezoidP

rectangle=

( )( )( )( )

118 16 34

228 50

+=

450

1400= 0.32

Examples

3. One of the two squares

2 squaresP

rectangle=

( )( )( )

22 10

28 50=

200

1400= 0.14