EXAMPLE 1 Use lengths to find a geometric probability

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Presentation transcript:

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

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?

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).

Use a segment to model a real-world probability 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.

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

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. SOLUTION Length of RT Length of PQ P(Point is on RT) = 2 ( 1) 5 ( 5) – = = 1 10 , 0.1, 10%

GUIDED PRACTICE for Examples 1 and 2 2. TS Length of TS Length of PQ P(Point is on TS) = 1( 4) 5 ( 5) – = = 1 2 , 0.5, 50% 3. PT Length of PT Length of PQ P(Point is on PT) = 5 ( 1) 5 ( 5) – = = 2 5 , 0.4, 40%

GUIDED PRACTICE for Examples 1 and 2 4. RQ Length of RQ Length of PQ P(Point is on RQ) = 2 ( 5) 5 ( 5) – = = 7 10 , 0.7, 70%

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? SOLUTION STEP 1 Find the longest you can wait for the monorail and still get to the station near your work by 8:43. 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 6 minutes (8:49 – 8:43 = 6 min).

GUIDED PRACTICE for Examples 1 and 2 STEP 2 Model the situation. The monorail runs every 12 minutes, so you need it to arrive within 6 minutes. STEP 3 Find the probability. P(you get to the station by 8:43) Favorable waiting time Maximum waiting time = 6 12 = = 1 2 The probability that you will get to the station by 8:58. is 1 2 or 50%.