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

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

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

  9. 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? 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).

  10. P(you get to the station by 8:43) Favorable waiting time 6 1 = = = Maximum waiting time 12 2 The probability that you will get to the station by 8:58. is 1 or 50%. 2 for Examples 1 and 2 GUIDED PRACTICE 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.

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