Question

each letter of the alphabet is written on a piece of paper and put in a hat. if a piece of paper is chosen at random, what is the probability that it will be a vowel? the number of favorable outcomes is. the number of possible outcomes is. so ( p(\text{vowel}) = ), or about percent.

Explanation:

Step1: Determine favorable outcomes

Vowels in English alphabet: a, e, i, o, u. So number of favorable outcomes = 5.

Step2: Determine possible outcomes

There are 26 letters in English alphabet. So number of possible outcomes = 26.

Step3: Calculate probability

Probability formula: \(P=\frac{\text{favorable outcomes}}{\text{possible outcomes}}\). So \(P(\text{vowel})=\frac{5}{26}\).

Step4: Convert to percentage

\(\frac{5}{26}\approx0.1923\). Multiply by 100: \(0.1923\times100 = 19.23\%\).

Answer:

The number of favorable outcomes is \(5\).
The number of possible outcomes is \(26\).
So \(P(\text{vowel})=\frac{5}{26}\), or about \(19.23\) percent.