Chapter 6.7, Problem 12E

a.

To determine

To calculate: The probability that the letter chosen is E or an X.

Answer to Problem 12E

The probability that the letter chosen is E or an X is $\frac{1}{3}$

Explanation of Solution

Given information:

A letter in the word EXPERIMENTAL is chosen

Calculation:

To find the probability that the letter chosen is E or an X, find the probability of getting an E and the probability of getting an X and add them.

  $\begin{array}{l}P(\text{E is chosen)=}\frac{\text{Number of E in the word }}{\text{Total number of letters in the word}}\\ \text{ =}\frac{3}{12}\\ \end{array}$

  $\begin{array}{l}P(X\text{ is chosen)=}\frac{\text{Number of X in the word }}{\text{Total number of letters in the word}}\\ \text{ =}\frac{1}{12}\\ \end{array}$

  $\begin{array}{l}P(\text{choosing an E or X)=}\frac{3}{12}+\frac{1}{12}\text{ [Add]}\\ \text{ =}\frac{4}{12}\text{ [Express in simplest form]}\\ \text{ =}\frac{1}{3}\end{array}$

b.

To determine

To calculate: The probability that the letter chosen is vowel or a consonant.

Answer to Problem 12E

The probability that the letter chosen is vowel or a consonant is $1$ .

Explanation of Solution

Given information:

A letter in the word EXPERIMENTAL is chosen

Calculation:

To find the probability that the letter chosen is vowel or a consonant, find the probability of getting a vowel and the probability of getting a consonant and add them.

  $\begin{array}{l}P(\text{vowel is chosen)=}\frac{\text{Number of vowels in the word }}{\text{Total number of letters in the word}}\\ \text{ =}\frac{5}{12}\\ \end{array}$

  $\begin{array}{l}P(\text{consonat is chosen)=}\frac{\text{Number of consonants in the word }}{\text{Total number of letters in the word}}\\ \text{ =}\frac{7}{12}\\ \end{array}$

  $\begin{array}{l}P(\text{choosing a vowel or consonant)=}\frac{5}{12}+\frac{7}{12}\text{ [Add]}\\ \text{ =}\frac{12}{12}\text{ [Express in simplest form]}\\ \text{ =1}\end{array}$

c.

To determine

To calculate: The probability that the letter chosen is from the first half of the alphabet(A-M) or second part of the alphabet.

Answer to Problem 12E

The probability that the letter chosen is from the first half of the alphabet(A-M) or second part of the alphabetis $\frac{6}{13}$

Explanation of Solution

Given information:

A letter in the word EXPERIMENTAL is chosen

Calculation:

To find the probability that the letter chosen is from the first half of the alphabet(A-M) or second part of the alphabet(N-Z), find the probability of choosing a letter from the first half of the alphabet and choosing a letter from the second part of the alphabet and add them.

  $\begin{array}{l}P(\text{letter from A to M is chosen) =}\frac{\text{Number of letters from A to M in the word }}{\text{Total number of letters}}\\ \text{ =}\frac{7}{26}\\ \end{array}$

  $\begin{array}{l}P(\text{letter from the N to Z is chosen) =}\frac{\text{Number of letters from N to Z in the word }}{\text{Total number of letters }}\\ \text{ =}\frac{5}{26}\\ \end{array}$

  $\begin{array}{l}P(\text{choosing a letter from A to M or N to Z )=}\frac{7}{26}+\frac{5}{26}\text{ [Add]}\\ \text{ =}\frac{12}{26}\text{ [Express in simplest form]}\\ \text{ = }\frac{6}{13}\\ \end{array}$