Section 7-8 Geometric Probability
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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

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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


length of favorable segment

length of entire segment

8

12

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) =

2

3

=

=


Represent this using a segment.

3

4

P(waiting more than 15 minutes) = , or

45

60

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.

3

4

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.

20 cm

Find the area of the square.

A = s2 = 202 = 400 cm2

..continued


area between square and circle length

area of square

400 – 100

400

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) =

= 0.2146

The probability that a dart landing randomly in the square does not land

within the circle is about 21.5%.


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