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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

3. Geometric Probability

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Exercise 42 Page 937

a A spinner is divided into

8

equal sections. We want to find the probability that if the arrow lands on a number, it will land on

3 .

We will use geometric probability. The probability of the arrow landing on

3

is the ratio of the area of the section corresponding to

3

to the area of the spinner.

Let's call the area of the spinner

A .

Since the spinner is divided into

8

equal sections, the area of each section, including the section corresponding to the number

3,

is

\frac{1}{8} A .

Therefore, the probability that the arrow lands on

3

is the ratio of

\frac{1}{8} A

to

A .

P (arrow lands on 3) = \frac{\frac{1}{8} A}{A}

MovePartNumLeft

$\frac{a \cdot b}{c} = a \cdot \frac{b}{c}$

P (arrow lands on 3) = \frac{1}{8} \frac{A}{A}

$\frac{a}{a} = 1$

P (arrow lands on 3) = \frac{1}{8}

The probability that the arrow lands on

3

is

\frac{1}{8} .

b We want to find the probability that if the arrow lands on a number, it lands on an odd number. We will use geometric probability. The probability of the arrow landing on an odd number is the ratio of the area of sections corresponding to odd numbers to the area of the spinner.

As we can see, there are

4

odd numbers on the spinner. We already know from Part A that if we call the area of the spinner

A,

each section has area

\frac{1}{8} A .

This means that the combined area of all the sections corresponding to odd numbers is

\frac{4}{8} A .

Therefore, our probability is the ratio of

\frac{4}{8} A

to

A .

P (arrow lands on odd number) = \frac{\frac{4}{8} A}{A}

MovePartNumLeft

$\frac{a \cdot b}{c} = a \cdot \frac{b}{c}$

P (arrow lands on odd number) = \frac{4}{8} \frac{A}{A}

$\frac{a}{a} = 1$

P (arrow lands on odd number) = \frac{4}{8}

$\frac{a}{b} = \frac{a / 4}{b / 4}$

P (arrow lands on odd number) = \frac{1}{2}

The probability that the spinner will land on an odd number is

\frac{1}{2} .

Subchapter links

Check Your Understanding p.934

Practice and Problem Solving p.934-936

H.O.T. Problems p.936

Standardized Test Practice p.937

Spiral Review p.937

Skills Review p.937