1. EXAMPLE 1 Use lengths to find a geometric probability SOLUTION Find the probability that a point chosen at random on PQ is on RS. 0.6, or 60%. Length of RS Length of PQ P (Point is on RS ) = = 6 10, = 3 5 4 ( 2) 5 ( 5) –– = ––

2. EXAMPLE 2 Use a segment to model a real-world probability MONORAIL A monorail runs every 12 minutes. The ride from the station near your home to the station near your work takes 9 minutes. One morning, you arrive at the station near your home at 8:46. You want to get to the station near your work by 8:58. What is the probability you will get there by 8:58 ?

3. EXAMPLE 2 Use a segment to model a real-world probability SOLUTION STEP 1 Find: the longest you can wait for the monorail and still get to the station near your work by 8:58. The ride takes 9 minutes, so you need to catch the monorail no later than 9 minutes before 8:58, or by 8:49. The longest you can wait is 3 minutes ( 8:49 – 8:46 = 3 min ).

4. EXAMPLE 2 Use a segment to model a real-world probability STEP 2 Model the situation. The monorail runs every 12 minutes, so it will arrive in 12 minutes or less. You need it to arrive within 3 minutes. The monorail needs to arrive within the first 3 minutes.

5. EXAMPLE 2 Use a segment to model a real-world probability STEP 3 Find: the probability. P (you get to the station by 8:58 ) Favorable waiting time Maximum waiting time = 3 12 = = 1 4 The probability that you will get to the station by 8:58. is 1 4 or 25%. ANSWER

6. GUIDED PRACTICE for Examples 1 and 2 Find the probability that a point chosen at random on PQ is on the given segment. Express your answer as a fraction, a decimal, and a percent. RT 1., 0.1, 10% ANSWER 1 10

7. GUIDED PRACTICE for Examples 1 and 2 2. TS 1 2, 0.5, 50% ANSWER Find the probability that a point chosen at random on PQ is on the given segment. Express your answer as a fraction, a decimal, and a percent.

8. GUIDED PRACTICE for Examples 1 and 2 3. PT 2 5, 0.4, 40% ANSWER Find the probability that a point chosen at random on PQ is on the given segment. Express your answer as a fraction, a decimal, and a percent.

9. GUIDED PRACTICE for Examples 1 and 2 4. RQ 7 10, 0.7, 70% ANSWER Find the probability that a point chosen at random on PQ is on the given segment. Express your answer as a fraction, a decimal, and a percent.

10. GUIDED PRACTICE for Examples 1 and 2 5. WHAT IF? In Example 2, suppose you arrive at the station near your home at 8:43. What is the probability that you will get to the station near your work by 8:58 ? 1 2 or 50%. ANSWER