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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 15 Page 937

The ratio of the area of a sector of a circle to the area of the entire circle is the same as the ratio of the central angle of the sector to 360.

1/4 or 25 %

Probability that involves a geometric measure such as length or area is called geometric probability. Suppose that a region A contains a region B.

regions

Suppose now that a point Q in region A is chosen at random. Then, the probability that point Q is in region B is given by the ratio of the area of region B to the area of region A.

P(Qis inB)=Area of regionB/Area of regionA We can also use angle measures to find geometric probability. The ratio of the area of a sector of a circle to the area of the entire circle is the same as the ratio of the central angle of the sector to 360. With this in mind, let's consider the given diagram.

We want to find the probability of the pointer landing on red. We can see that the angle measure of the red region is equal to 90^(∘). We can use this value to create a ratio out of 360.

P(Red) = 90/360

a/b=.a /90./.b /90.

P(Red) = 1/4

▼

Convert to percent

Write as a decimal

P(Red) = 0.25

Convert to percent

P(Red) = 25 %

The probability of the pointer landing on red is 14, which can be also written as 25 %.