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