Obj. 48 Geometric Probability

• 1. Obj. 48 Geometric Probability The student is able to (I can): Calculate geometric probabilites Use geometric probability to predict results in real-world situations

2. theoretical probabilityIf every outcome in a sample space is equally likely to occur, then the theoretical probability of an event is P=geometric probabilitynumber of outcomes in the event number of outcomes in the sample spaceThe 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. 3. ExamplesA point is chosen randomly on RD . Find the probability of each event. 4 R3EA5 D1. The point is on RA . RA 7 P= = RD 12 2. The point is not on RE .RE P (not RE ) = 1 P ( RE ) = 1 RD 4 8 2 = 1 = = 12 12 3 4. ExamplesA 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?P=5 1 = 60 12 5. Examples 20E 102. If you arrive at the light 50 times, predict about how many times you will have to wait more than 10 seconds. CE 20 1 = = P= AD 60 3 Therefore, if you arrive at the light 50 times, you will probably stop and wait more than 10 seconds about 1 ( 50 ) 17 times 3 6. ExamplesUse the spinner to find the probability of each event. 1. Landing on red 80 2 P= = 360 9 2. Landing on purple or blue75 + 60 135 3 P= = = 360 360 8 3. Not landing on yellow 360 100 260 13 P= = = 360 360 18 7. ExamplesFind the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth.1. The circle ( 92 ) circle P= = 0.18 rec tangle ( 28 )( 50 ) 8. Examples2. The trapezoid 1 18 16 + 34 ) trapezoid 2 ( )( = P= ( 28 )( 50 ) rec tangle =450 0.32 1400 9. Examples3. One of the two squares2 ( 102 )2 squares = P= ( 28 )( 50 ) rec tangle =200 0.14 1400