Use geometric probability to predict results in real-world situations

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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

If an event has a probability p of occurring, the probability of the event not occurring is 1 – p. Remember!

A point is chosen randomly on PS. Find the probability of each event. Example 1 A point is chosen randomly on PS. Find the probability of each event. 1 5 The point is on RS. The point is not on QR. 12 25 The point is on PQ or QR. 4 5

Example 3 A radio station gives a weather report every 10 minutes. Each report last 45 seconds. Suppose you turn on the station at random. What is the probability the report will be on when you turn on the radio 45 600 = .075 If you turn on the radio 50 times, predict about how many times you will have wait more than 5 minutes to hear the report

Example 2 A pedestrian signal at a crosswalk has the following cycle: “green” for 25 seconds, “yellow” for 5 seconds and “red” for 30 seconds. What is the probability the signal will show “yellow” when you arrive? 1 12 = .083 If you arrive at the signal 50 times, predict about how many times you will have to stop and wait more than 10 seconds. If you follow the traffic laws and waiting is when its red, you will be stopped for more than 10 for 20 seconds 20 60 = 1 3 1 3 of 50 ≈ 17 times

Example 3 Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth. the circle the trapezoid one of the two squares