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EXAMPLE 1

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

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EXAMPLE 1

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

  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. 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. EXAMPLE 2 Use a segment to model a real-world probability STEP 2 The monorail needs to arrive within the first 3 minutes.

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

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

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

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

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

  10. ANSWER 1 or 50%. 2 for Examples 1 and 2 GUIDED PRACTICE 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?

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