section 7-8 geometric probability spi 52a: determine the probability of an event objectives: use...
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Section 7-8 Geometric Probability SPI 52A: determine the probability of an event
Objectives:• use segment and area models to find the probability of events
Geometric Probability:• Let points on a number line represent outcomes• Find probability by comparing measurements of sets of points
P(event) = length of favorable segment length of entire segment
The length of the segment between 2 and 10 is 10 – 2 = 8.
The length of the ruler is 12.
P(landing between 2 and 10) =
length of favorable segmentlength of entire segment
812
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A gnat lands at random on the edge of the ruler below.
Find the probability that the gnat lands on a point
between 2 and 10.
Finding Probability using Segments
= =
A museum offers a tour every hour. If Benny arrives at the tour site at a
random time, what is the probability that he will have to wait at least 15
minutes?
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 Benny’s waiting more than 15 minutes.
P(waiting more than 15 minutes) = , or 4560
34
Represent this using a segment.
The probability that Benny will have to wait at least 15 minutes is , or 75%.34
Real-World: Finding Probability
Find the area of the square.A = s2 = 202 = 400 cm2
Find the area of the circle. Because the square has sides of length 20 cm, the circle’s diameter is 20 cm, so its radius is 10 cm.A = r 2 = (10)2 = 100 cm2
Find the area of the region between the square and the circle.A = (400 – 100 ) cm2
A circle is inscribed in a square target with 20-
cm sides. Find the probability that a dart
landing randomly within the square does not
land within the circle.
Finding Probability using Area
20 cm
Use areas to calculate the probability that a dart landing randomly in the square does not land within the circle. Use a calculator. Round to the nearest thousandth.
The probability that a dart landing randomly in the square does not land within the circle is about 21.5%.
P (between square and circle) =
= 0.2146
area between square and circlearea of square
400 – 100 400