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§10.6, Geometric Probability. Learning Targets. I will calculate geometric probabilities. I will use geometric probability to predict results in real-world situations. Vocabulary. geometric probability. - PowerPoint PPT Presentation
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§10.6, Geometric Probability
Learning TargetsI will calculate geometric probabilities.
I will use geometric probability to predict results in real-world situations.
Vocabulary
geometric probability
Remember that in probability, the set of all possible outcomes of an experiment is called the sample space. Any set of outcomes is called an event.
If every outcome in the sample space is equally likely, the theoretical probability of an event is
Geometric probability is used when an experiment has an infinite number of outcomes. In geometric probability, the probability of an event is based on a ratio of geometric measures such as length or area. The outcomes of an experiment may be points on a segment or in a plane figure.
10-6
10-6
A point is chosen randomly on PS. Find the probability of each event.
The point is on RS. The point is on QS.
25
18
PS
QSP
The point is not on QR. The point is not on RS.
25
7
25
1811
PS
QSP
10-6
Use the figure below to find the probability that the point is on BD.
10-6
A pedestrian signal at a crosswalk has the following cycle: “WALK” for 45 seconds and “DON’T WALK” for 70 seconds.
What is the probability the signal will show “WALK” when you arrive?
To find the probability, draw a segment to represent the number of seconds that each signal is on.
The signal is “WALK” for 45 out of every 115 seconds.
0 45 115
45 70
If you arrive at the signal 40 times, predict about how many times you will have to stop and wait more than 40 seconds.
In the model, the event of stopping and waiting more than 40 seconds is represented by a segment that starts at B and ends 40 units from C. The probability of stopping and waiting more than 40 seconds is
If you arrive at the light 40 times, you will probably stop and wait more than 40 seconds about
(40) ≈ 10 times.
B
70
115
300
C023
6
115
30P
10-6
A traffic light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. When you arrive at the light was is the probability that it is green?
12
5
60
25)( greenP
10-6
Use the spinner to find the probability of the pointer landing on yellow.
The angle measure in the yellow region is 140°.
the pointer landing on blue or red
the pointer not landing on green
10-6
Find the probability that a point chosen randomly inside the rectangle is in each shape. Round to the nearest hundredth.
the circle
The area of the circle is A = r2
= (9)2 = 81 ≈ 254.5 ft2.
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The probability is P = 254.51400
≈ 0.18.
10-6
the trapezoid
The area of the rectangle is A = bh = 50(28) = 1400 ft2.
The area of the trapezoid is
The probability is
10-6
one of the two squares
The area of the two squares is A = 2s2
= 2(10)2 = 200 ft2.
The area of the rectangle is A = bh= 50(28) = 1400 ft2.
The probability is
10-6
EXIT CHECK
A point is chosen randomly on EH. Find the probability of each event.
1. The point is on EG.
2. The point is not on EF.
35
1315
3. An antivirus program has the following cycle: scan: 15 min, display results: 5 min, sleep: 40 min. Find
the probability that the program will be scanning when you arrive at the computer. 0.25
5. Find the probability that a point chosen randomly inside the rectangle is in the triangle.
0.25
EXIT CHECK
4. Use the spinner to find the probability of the pointer landing on a shaded area.
0.5
HOMEWORK:
Page 721, #18 – 24, 27, 28, 38
