Transcript geometric probability

Geometric Probability
Homework: Geometric Probability WS 1
Objectives
Calculate geometric probabilities.
Use geometric probability to predict
results in real-world situations.
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.
Remember!
If an event has a probability p of occurring, the
probability of the event not occurring is 1 – p.
Geometric Probability
Process:
• Complete the experimental probabilities of landing
in the shaded regions of each figure.
• Then, determine the theoretical probability of
landing in the shaded areas of each figure.
– What is the area of the whole area?
– What is the area of the shaded regions?
– What is the probability of landing in the shading?
• Be sure to show all of your calculations!
• Give your answer as a fraction, decimal, & percent.
Example 1A: Using Length to Find Geometric
Probability
A point is chosen randomly on PS. Find the
probability of each event.
The point is on RS.
Example 1B: Using Length to Find Geometric
Probability
The point is not on QR.
Subtract from 1 to find the probability that the
point is not on QR.
Example 1C: Using Length to Find Geometric
Probability
The point is on PQ or QR.
P(PQ or QR) = P(PQ) + P(QR)
Check It Out! Example 1
Use the figure below to find the probability
that the point is on BD.
Example 2A: Transportation Application
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.
Example 2B: Transportation Application
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.
Check It Out! Example 2
Use the information below. What is the
probability that the light will not be on red
when you arrive?
The probability that the light will be on red is
Example 3A: Using Angle Measures to Find
Geometric Probability
Use the spinner to find the probability of each
event.
the pointer landing on yellow
The angle measure in the
yellow region is 140°.
Example 3B: Using Angle Measures to Find
Geometric Probability
Use the spinner to find the probability of each
event.
the pointer landing on blue or red
The angle measure in the blue region is 52°.
The angle measure in the red region is 60°.
Example 3C: Using Angle Measures to Find
Geometric Probability
Use the spinner to find the probability of each
event.
the pointer not landing on green
The angle measure in the green region is 108°.
Subtract this angle measure from 360°.
Check It Out! Example 3
Use the spinner below to find the probability
of the pointer landing on red or yellow.
The probability is
that the
spinner will land on red or
yellow.
Example 4: Using Area to find Geometric Probability
Find the probability that a point chosen
randomly inside the rectangle is in each shape.
Round to the nearest hundredth.
Example 4A: Using Area to find Geometric Probability
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 = 254.5 ≈ 0.18.
1400
Example 4B: Using Area to find Geometric Probability
the trapezoid
The area of the trapezoid is
The area of the rectangle is A = bh
= 50(28) = 1400 ft2.
The probability is
Example 4C: Using Area to find Geometric Probability
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
Check It Out! Example 4
Find the probability that a point chosen
randomly inside the rectangle is not inside the
triangle, circle, or trapezoid. Round to the
nearest hundredth.
Area of rectangle: 900 m2
The probability of landing
inside the triangle (and
circle) and trapezoid is
0.29.
Probability of not landing in
these areas is 1 – 0.29 =
0.71.
Geometric Probability
• What is the chance that a random point
picked would be in the shaded area of this
circle?
3 cm
10 cm
Challenge
What is the probability of hitting a shaded
area in terms of r = 4.5, the radius?
r
Lesson Quiz: Part I
A point is chosen randomly on EH. Find the
probability of each event.
1. The point is on EG.
3
5
2. The point is not on EF.
13
15
Lesson Quiz: Part II
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
4. Use the spinner to find the probability of the
pointer landing on a shaded area.
0.5
Lesson Quiz: Part III
5. Find the probability that a point chosen
randomly inside the rectangle is in the triangle.
0.25