Chapter 5, Problem 1RE

(a)

1. a. Which among the following numbers could be the probability of an event?

0, −0.01, 0.75, 0.41, 1.34

1. b. Which among the following numbers could be the probability of an event?

$\frac{2}{5},\frac{1}{3},-\frac{4}{7},\frac{4}{3},\frac{6}{7}$

To determine

To identify: The numbers that represents probability of an event.

Answer to Problem 1RE

The numbers that represent probability of an event are 0, 0.75, and 0.41.

Explanation of Solution

Given info:

The numbers are 0, -0.01, 0.75, 0.41, and 1.34.

Justification:

Rules of Probability:

• The probability of an event must lie between 0 and 1, inclusive.
• The sum of probabilities of all the outcomes is 1.

Here, it is observed that the numbers 0, 0.75, and 0.41 are lie between 0 and 1, inclusive. Hence, they represent the probabilities.

The values –0.01 and 1.34 does not lies between 0 and 1. That is, $-0.01<0$ and $1.34>1$.

Thus, the numbers represents probabilities are $\underset{\_}{\left\{\text{0, 0}\text{.75, 0}\text{.41}\right\}}$.

To determine

To identify: The numbers that represents probability of an event.

Answer to Problem 1RE

The numbers that represent probability of an event are $\underset{\_}{\frac{2}{5}}$, $\underset{\_}{\frac{1}{3}}$, and $\underset{\_}{\frac{6}{7}}$.

Explanation of Solution

Given info:

The numbers are $\frac{2}{5}$, $\frac{1}{3}$, $-\frac{4}{7}$, $\frac{4}{3}$ and $\frac{6}{7}$.

Justification:

Here, it is observed that the numbers $\frac{2}{5}$, $\frac{1}{3}$ , and $\frac{6}{7}$ are lie between 0 and 1, inclusive.

Hence, they represent the probabilities.

The values $-\frac{4}{7}$ and $\frac{4}{3}$ does not lies between 0 and 1. That is, $-\frac{4}{7}<0$ and $\frac{4}{3}>1$.

Hence, the values $-\frac{4}{7}$ and $\frac{4}{3}$ does not lies between 0 and 1.

Thus, the numbers represents probabilities are $\underset{\_}{\left\{\frac{2}{5}\text{, }\frac{1}{3}\text{, }\frac{6}{7}\right\}}$.