Question

if you randomly select a letter from the phrase \mathletes rule the world,\ what is the probability that you select a vowel? (your answer must be in the form of a reduced fraction.)

Explanation:

Step1: Count total letters

Count all letters in "Mathletes rule the world".
There are \(21\) letters (\(M - a - t - h - l - e - t - e - s - \space - r - u - l - e - \space - t - h - e - \space - w - o - r - l - d\)).

Step2: Count vowels

Count vowels (\(a,e,u,e,e,o\)). There are \(6\) vowels.

Step3: Calculate probability

Probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
So \(P = \frac{6}{21}\).

Step4: Simplify fraction

Divide numerator and denominator by \(3\). \(\frac{6\div3}{21\div3}=\frac{2}{7}\).

Answer:

\(\frac{2}{7}\)