IXL - Geometric probability (Geometry practice)

A point on

is chosen at random. What is the probability it is also on

Simplify your answer and write it as a proper fraction.

ref_doc_title.

Learn with an example

question

The central angle of sector Q is 72°. What is the probability that the spinner lands on Q?

Simplify your answer and write it as a proper fraction.

key idea

Probability is the measure of how likely an event is to occur.

If a region is completely contained in another and a point in the larger region is chosen at random, the probability it is in the smaller region equals the area of the smaller region divided by the area of the larger region.

If a point Z in region X is chosen at random, the probability that Z is in region Y is:

(

Z is in region Y

)

Area of region Y

Area of region X

A sector is the part of a circle enclosed by two radii and their intercepted arc. It is shaped like a slice of pie. The formula for the area of a sector is

360

where

is the area of the sector,

is the measure in degrees of the central angle of the sector, and

is the area of the circle.

solution

Look at the diagram.

To find the probability that the spinner lands on Q, divide the area of sector Q by the area of the circle. For now, call the area of the circle

Since the central angle of sector Q is 72°, the area of the sector is

360

Next, divide the area of sector Q by the area of the circle and simplify.

(

landing on Q

)

Area of sector Q

Area of the circle

360

So, the probability that the spinner lands on Q is

360

which is

Looking for more? Try these:

Lesson: Probability

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Teacher tools

Work it out

Not feeling ready yet? These can help:

B.4Lengths of segments on number lines

W.7Area of sectors

AA.1Theoretical and experimental probability

Lesson: Probability

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