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
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Section 7-8 Geometric Probability SPI 52A: determine the probability of an event
length of favorable segment
length of entire segment
Finding Probability using Segments
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.
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) =
Represent this using a segment.
P(waiting more than 15 minutes) = , or
Real-World: Finding Probability
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.
The probability that Benny will have to wait at least 15 minutes is , or 75%.
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
Finding Probability using Area
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.
Find the area of the square.
A = s2 = 202 = 400 cm2
area between square and circle
area of square
400 – 100
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.
P (between square and circle) =
The probability that a dart landing randomly in the square does not land
within the circle is about 21.5%.