Exercise 19 Page 962

We are told that a spinner numbered $1$ to $8$ is spun.

Recall that the experimental probability of an event measures the likelihood that the event occurs based on the actual results of an experiment.

P (Event) = \frac{Number of times the event occurs}{Number of times the experiment is done}

We want to find the probability of not landing on

5 .

Note that this is the complement of spinner landing on

5 .

The sum of the probability of an event and the probability of its complement is

1 .

P (Event) + P (Not event) = 1

Let's start by finding the probability of a spinner landing on a

5,

which will be our event. The number of times the experiment is done is the total number of parts on the spinner,

8 .

The number of times the event occurs is the number of parts of the spinner numbered

5 .

There is

1

part numbered 5 on the spinner. Now, we can write

P (5) .

P (5) = \frac{1}{8} \leftarrow \leftarrow Part number 5 Total parts

The experimental probability of landing on part

5

is

\frac{1}{8} .

Let's now find the probability of its complement, which is landing on a part that is not numbered

5 .

P (5) + P (Not 5) = 1

$P (5) = \frac{1}{8}$

\frac{1}{8} + P (Not 5) = 1

▼

Solve for

P (Not 5)

$LHS - \frac{1}{8} = RHS - \frac{1}{8}$

P (Not 5) = 1 - \frac{1}{8}

Rewrite $1$ as $\frac{8}{8}$

P (Not 5) = \frac{8}{8} - \frac{1}{8}

Subtract fractions

P (Not 5) = \frac{7}{8}

▼

Convert to percent

Write as a decimal

P (Not 5) = 0.875

Convert to percent

P (Not 5) = 87.5 %

We found that

P (Not 5)

is

\frac{1}{8},

whhich can be also written as

87.5 % .