Q18. - Algebra 1

Question

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

P(a vowel)

Step-by-Step Solution

Answer

The odds of getting a vowel when a letter is chosen from the given name is $\frac{11}{24}$.

Step 1. Apply the basic formula for probability.

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

$\text{Probability of an outcome}=\frac{\text{number of favorite outcome}}{\text{total outcome}}$

Step 2. Write the given information.

From the given information it can be seen that there are 24 letters in the given name, and the desired outcome that is the number of vowels in the name are 11(E,U,I,E,A,E,O,A,E,I,A).

 

Hence the number of favorite outcome is 11 and total outcomes are 24.

Step 3. DESCRIPTION OF STEP.

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

$\mathrm{P}\left(\text{a vowel}\right)=\frac{11}{24}$

Thus, the odds of getting a vowel when a letter is chosen from the given name is $\frac{11}{24}$.