Q19. - Algebra 1

Question

Find the odds of each outcome if a computer randomly picks a letter in the name THE UNITED STATES OF AMERICA.

A consonant

Step-by-Step Solution

Answer

The odds of getting a consonant when a letter is chosen from the given name is $\frac{13}{24}$.

Step 1. Apply the basic formula for probability.

The probability of an event is given by the following formula:

Step 2. Write the given information.

From the given information it can be seen that there are 24 letters in the given name, and note that there are 11 vowels (E, U, I, E, A, E, O, A, E, I, A) in the name, i.e., the number of consonants in the name are:

$24-11=13$

Thus, the number of favorite outcomes is 13 and the total outcomes are 24.

Step 3. DESCRIPTION OF STEP.

Substitute the number of favorite outcomes and total outcomes in the formula.

$P\left(\text{a consonant}\right)=\frac{13}{24}$

Thus, the odds of getting a vowel when a letter is chosen from the given name is $\frac{13}{24}$.