Introduction to Basic Probability
Probability measures the likelihood of an event occurring. In its simplest form, the probability $P$ of an event $E$ is calculated using the formula:
$$P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$
Solving the Problem
In the English alphabet, there are a total of 26 letters. We want to find the probability of selecting a vowel and a consonant.
1. The Total Sample Space
The set of all outcomes consists of the 26 letters of the English alphabet: $S = \{A, B, C, \dots, Z\}$. Thus, the total number of possible outcomes is $26$.
2. Probability of selecting a Vowel
There are 5 vowels in the English alphabet: $\{A, E, I, O, U\}$. Using our probability formula:
$$P(\text{vowel}) = \frac{5}{26}$$
3. Probability of selecting a Consonant
There are 21 consonants in the English alphabet. Alternatively, we can use the complement rule since every letter is either a vowel or a consonant:
$$P(\text{consonant}) = 1 - P(\text{vowel}) = 1 - \frac{5}{26} = \frac{21}{26}$$
Summary of Results
- The probability of picking a vowel is $\frac{5}{26} \approx 0.192$.
- The probability of picking a consonant is $\frac{21}{26} \approx 0.808$.