Geometric Probability

1
Geometric Probability
GEOMETRY LESSON 7-8
The length of the segment between 2 and 10 is 10
2 8.
The length of the ruler is 12.
2
Geometric Probability
GEOMETRY LESSON 7-8
Because the favorable time is given in minutes,
write 1 hour as 60 minutes. Benny may have to
wait anywhere between 0 minutes and 60 minutes.
Starting at 60 minutes, go back 15 minutes. The
segment of length 45 represents Bennys waiting
more than 15 minutes.
3
Geometric Probability
GEOMETRY LESSON 7-8
Find the area of the square. A s2 202 400
cm2
4
Geometric Probability
GEOMETRY LESSON 7-8
The probability that a dart landing randomly in
the square does not land within the circle is
about 21.5.
5
Geometric Probability
GEOMETRY LESSON 7-8
To win a prize, you must toss a quarter so that
it lands entirely within the outer region of the
circle below. Find the probability that this
happens with a quarter of radius in. Assume
that the quarter is equally likely to land
anywhere completely inside the large circle.
15 32
6
Geometric Probability
GEOMETRY LESSON 7-8
(continued)
15 32
Find the area of the circle with a radius of 9
in. A r2 (9 )2 281.66648 in.2
15 32
7
Geometric Probability
GEOMETRY LESSON 7-8
The probability that the quarter lands entirely
within the outer region of the circle is about
0.326, or 32.6.
8
Geometric Probability
GEOMETRY LESSON 7-8
1. A point on AF is chosen at random. What is the
probability that it is a point on BE?
2. Express elevators to the top of a tall
building leave the ground floor every 40
seconds. What is the probability that a
person would have to wait more than 30 seconds
for an express elevator? A dart you throw is
equally likely to land at any point on each
board shown. For Exercises 35, find the
probability of its landing in the shaded
area. 3. regular octagon 4. square 5. circle
3 5
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