1. 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%.

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. 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.

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

7. 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%

8. 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%

9. 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).

10. 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%.