Let's analyze the given probability and find the complement event step by step.
We are given the probability that an event does not occur (specifically, the event that is "not yellow"):
[tex]\[ P(\text{not yellow}) = \frac{4}{15} \][/tex]
The complement of "not yellow" is "yellow". To find the probability of the complement event (yellow), we use the complement rule in probability. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening:
[tex]\[ P(\text{yellow}) = 1 - P(\text{not yellow}) \][/tex]
Substituting the given probability into the complement rule:
[tex]\[ P(\text{yellow}) = 1 - \frac{4}{15} \][/tex]
Now, let's perform the subtraction:
[tex]\[ P(\text{yellow}) = 1 - \frac{4}{15} \][/tex]
First, we convert 1 to a fraction with a common denominator of 15:
[tex]\[ 1 = \frac{15}{15} \][/tex]
Then, subtract the fractions:
[tex]\[ P(\text{yellow}) = \frac{15}{15} - \frac{4}{15} = \frac{15 - 4}{15} = \frac{11}{15} \][/tex]
Thus, the probability of the complement event (yellow) is:
[tex]\[ P(\text{yellow}) = \frac{11}{15} \][/tex]
The correct answer to the question is:
[tex]\[ P(\text{yellow}) = \frac{11}{15} \][/tex]
