Find the probability that a point chosen at random     on
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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

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%.


Example 1

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 1

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).


Example 1

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.


Example 1

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.


Example 1

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


Example 1

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


Example 1

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


Example 1

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


Example 1

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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