To find the probability of the complement of an event, we need to understand that the sum of the probabilities of an event and its complement must equal 1. This is a fundamental concept in probability theory.
1. Given:
- The probability of the event [tex]\( P(\text{Event}) = \frac{2}{7} \)[/tex].
2. The probability of the complement of the event, [tex]\( P(\text{Complement}) \)[/tex], is calculated as:
[tex]\[
P(\text{Complement}) = 1 - P(\text{Event})
\][/tex]
3. Substitute the given probability into the equation:
[tex]\[
P(\text{Complement}) = 1 - \frac{2}{7}
\][/tex]
4. To perform the subtraction, convert 1 to a fraction with a denominator of 7:
[tex]\[
1 = \frac{7}{7}
\][/tex]
5. Now, subtract the fractions:
[tex]\[
P(\text{Complement}) = \frac{7}{7} - \frac{2}{7} = \frac{7 - 2}{7} = \frac{5}{7}
\][/tex]
Thus, the probability of the complement of the event is [tex]\(\frac{5}{7}\)[/tex].
Among the provided options, the correct answer is:
[tex]\(\frac{5}{7}\)[/tex].
