Chapter 9, Problem 1RE

(a)

To determine

The sample space S for the letters from the word “integral”.

Answer to Problem 1RE

Solution:

The sample space S for the letters from the word “integral” is $S=\left\{i,n,t,e,g,r,a,l\right\}$.

Explanation of Solution

Given Information:

The word “integral”.

Formula used:

In probability, the set of all possible outcomes of the experiment is the sample space of the experiment.

Consider the provided word “integral”.

The sample space of the letters from the word “integral” is the set of all eight letters present in the word “integral”. So, the sample space is:

$S=\left\{\text{i,n,t,e,g,r,a,l}\right\}$

Therefore, the sample space is $S=\left\{i,n,t,e,g,r,a,l\right\}$.

(b)

To determine

The outcomes of the event A that describe the set of vowel form the word integral.

Answer to Problem 1RE

Solution:

The outcomes of the event A that describe the set of vowel is $A=\left\{i,e,a\right\}$.

Explanation of Solution

Given Information:

The word “integral”.

Consider the provided word “integral”.

The sample space of the letters from the word “integral” is the set of all letters present in the word “integral”. So, the sample space is:

$S=\left\{\text{i,n,t,e,g,r,a,l}\right\}$

The event A is defined as that the letter is a vowel. The vowels that are present in the word “integral” are $i,e,a$. So, the possible outcomes of the event A is:

$A=\left\{i,e,a\right\}$

Therefore, The outcomes of the event A that describe the set of vowel is $A=\left\{i,e,a\right\}$.

(c)

To determine

The outcomes of the event A that describe the letter “g”.

Answer to Problem 1RE

Solution:

The outcomes of the event A that describe the letter “g” is $B=\left\{\text{g}\right\}$.

Explanation of Solution

Given Information:

The word “integral”.

Formula used:

In probability, the event is the sub collection or subset of a sample space.

Consider the provided word “integral”.

The sample space of the letters from the word “integral” is the set of all letters present in the word “integral”. So, the sample space is:

$S=\left\{i,n,t,e,g,r,a,l\right\}$

The event B is defined as that the letter is a “g”. So, the only possible outcome of the event B is:

$B=\left\{g\right\}$

Therefore, the outcomes of the event A that describe the letter “g” is $B=\left\{g\right\}$.