Chapter 5, Problem 1CR

Terminology Consider the following terms: sample space: event A; complement of event A.

Match each terms to the appropriate description.

(i) the event: that event A does not occur

(ii) collection of one or more outcomes of a statistical experiment or observation

(iii) set of all outcomes of a statistical experiment or observation

To determine

The correct match for the provided terms sample space, event A, and complement of event A with their appropriate descriptions.

Answer to Problem 1CR

Solution:

The correct match for the term ‘sample space’ is ‘set of all possible outcomes of a statistical experiment or observation’.

The correct match for the term ‘event A’ is ‘collection of one or more outcomes of a statistical experiment or observation’.

The correct match for the term ‘complement of event A’ is ‘the event that event A does not occur’.

Explanation of Solution

Given Information:

The provided descriptions are:

(i) The event that event A does not occur.

(ii) Collection of one or more outcomes of a statistical experiment or observation.

(iii) Set of all possible outcomes of a statistical experiment or observation.

Consider the term ‘sample space’ in which a particular outcome of a statistical experiment is known as a simple event. The set of all possible outcomes (simple events) of a statistical experiment constitutes the sample space of an experiment. It is denoted by ‘S’.

So, the correct match for the ‘set of all possible outcomes of a statistical experiment or observation’ is ‘sample space’.

Consider the term ‘event A’ that can be defined as the subset of a sample space that consists of a collection of one or more outcomes of an experiment. So, the correct match for the ‘collection of one or more outcomes of a statistical experiment or observation’ is ‘event A’.

Consider the term ‘complement of event A’. It can be defined as the event that event A does not occur. It can be denoted by ‘event $A^c$’. So, the correct match for the ‘complement of event A’ is ‘the event that event A does not occur’.