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, 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:

Identify the sample space and possible outcomes

The problem states that each letter of the alphabet is written on a piece of paper. The English alphabet consists of 26 letters: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z.
Therefore, the total number of possible outcomes is 26.

Identify the favorable outcomes

We want to find the probability of choosing a vowel. The standard vowels in the English alphabet are A, E, I, O, and U.
Counting these letters:

• A, E, I, O, U

There are 5 vowels.
Therefore, the number of favorable outcomes is 5.

Calculate the probability as a fraction

The theoretical probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:

$$ P(\text{vowel}) = \frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}} = \frac{5}{26} $$

Convert the probability to a percentage

To find the percentage, we divide 5 by 26 and multiply by 100:

$$ \frac{5}{26} \approx 0.1923 $$

$$ 0.1923 \times 100\% \approx 19.2\% $$

Rounding to the nearest whole percent or standard decimal value typically used in such school exercises, \(19\) percent is the most common approximation (since \(19.2\%\) rounds to \(19\%\)).

Answer:

Each letter of the alphabet is written on a piece of paper and put in a hat. If a piece of paper is chosen, what is the probability that it will be a vowel?
The number of favorable outcomes is <blank>5</blank>.
The number of possible outcomes is <blank>26</blank>.
So \(P(\text{vowel}) =\) <blank>\(\frac{5}{26}\)</blank>, or about <blank>19</blank> percent.