Post on 16-Jul-2015
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