Obj. 41 Geometric Probability
- 1. Geometric Probability The student is able to (I can): • Calculate geometric probabilites • Use geometric probability to predict results in real-world situations
- 2. 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 event P number of outcomes in the sample space =
- 3. 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 ( ) = RA P RA RD 7 12 = RE ( ) ( )P not RE 1 P RE= − RE 1 RD = − 4 1 12 = − 8 2 12 3 = =
- 4. 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? ( ) = 5 P yellow 60 1 12 =
- 5. 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 CE P AD = 20 60 = 1 3 = ( ) 1 50 17 times 3 ≈
- 6. 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 80 P 360 = 2 9 = 75 60 P 360 + = 135 360 = 3 8 = 360 100 P 360 − = 260 360 = 13 18 =
- 7. Examples Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. 1. The circle circle P rectangle = ( ) ( )( ) 2 9 28 50 π = 0.18≈
- 8. Examples 2. The trapezoid trapezoid P rectangle = ( )( ) ( )( ) 1 18 16 34 2 28 50 + = 450 1400 = 0.32≈
- 9. Examples 3. One of the two squares 2 squares P rectangle = ( ) ( )( ) 2 2 10 28 50 = 200 1400 = 0.14≈