Chapter 10, Problem 1CRQ

Fill in the blanks.

1. a. An activity with observable results is called a/an ________.
2. b. The observable results are called _____ or _____ _____.
3. c. The totality of all outcomes is called a/an _____ _____.
4. d. The probability of an event is a number between _____ and _____.

To determine

To fill: The blank in the statement “An activity with observable results is called a/an ______” with the appropriate answer.

Answer to Problem 1CRQ

The completed statement is “An activity with observable results is called an $\underset{\_}{\text{experiment}}$”.

Explanation of Solution

Recall that, “An experiment is an activity with observable results called outcomes or the sample points”.

For example, while tossing a coin the possible outcome to land head is $\frac{1}{2}$ as well as the possible outcome to land tails is $\frac{1}{2}$.

Here, tossing a coin is an experiment.

Hence, “An activity with observable results is called an $\underset{\_}{\text{experiment}}$”.

To determine

To fill: The blank in the statement “The observable results are called ______ or _____” with the appropriate answer.

Answer to Problem 1CRQ

The completed statement is “The observable results are called $\underset{\_}{\text{outcomes}}$ or $\underset{\_}{\text{sample points}}$”.

Explanation of Solution

From part a., observe that while tossing a coin there will be a result, that is, the coin may land as head or tails.

Here, coin tossing is an experiment and head and tails are possible outcomes.

Hence, “The observable results are called $\underset{\_}{\text{outcomes}}$ or $\underset{\_}{\text{sample points}}$”.

To determine

To fill: The blank in the statement “The totality of all outcomes is called a/an _____” with the appropriate answer.

Answer to Problem 1CRQ

The completed statement is “The totality of all outcomes is called a $\underset{\_}{\text{sample space}}$”.

Explanation of Solution

Note that, the set of all possible outcomes of a random experiment is said to be a sample space of an experiment.

Moreover, an event is a subspace of the sample space of a random experiment.

That is, a sample space is a totality of all outcomes.

Hence, “The totality of all outcomes is called a $\underset{\_}{\text{sample space}}$”.

To determine

To fill: The blank in the statement “The probability of an event is a number between ____ and _____” with the appropriate answer.

Answer to Problem 1CRQ

The completed statement is “The probability of an event is a number between $\underset{\_}{0}$ and $\underset{\_}{1}$”.

Explanation of Solution

It is known that, “The discrete probability function P with the domain $\left\{x_1,x_2,\mathrm{...},x_n\right\}$ satisfies the condition $0\le P\left(x_i\right)\le 1,\text{ for }1\le i\le n$”.

That is, the probability $P\left(x_i\right)$ of an event will be between 0 and 1.

Hence, “The probability of an event is a number between $\underset{\_}{0}$ and $\underset{\_}{1}$”.