To find the probability of the complement of an event, we need to understand that the probabilities of an event and its complement must add up to 1. This is because either the event occurs, or it does not, and the total of all probabilities in a sample space is always 1.
Given that the probability of the event is [tex]\( \frac{2}{7} \)[/tex]:
1. Start with the total probability of the sample space, which is 1.
2. Subtract the probability of the event from the total probability to find the probability of the complement of the event.
Let's illustrate this step-by-step:
[tex]\[ P(\text{Complement of event}) = 1 - P(\text{Event}) \][/tex]
Given:
[tex]\[ P(\text{Event}) = \frac{2}{7} \][/tex]
So:
[tex]\[ P(\text{Complement of event}) = 1 - \frac{2}{7} \][/tex]
To perform the subtraction, we need to express 1 as a fraction with a denominator of 7:
[tex]\[ 1 = \frac{7}{7} \][/tex]
Now we can subtract:
[tex]\[ P(\text{Complement of event}) = \frac{7}{7} - \frac{2}{7} \][/tex]
This subtraction gives:
[tex]\[ P(\text{Complement of event}) = \frac{7 - 2}{7} = \frac{5}{7} \][/tex]
Therefore, the probability of the complement of the event is [tex]\( \frac{5}{7} \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{\frac{5}{7}} \][/tex]
