To determine the probability of the complement of a given event, we use the concept of complementary probabilities. The probability of an event and its complement sum to 1.
Given:
[tex]\[ P(\text{not yellow}) = \frac{\overline{15}}{15} \][/tex]
We first express [tex]\( P(\text{not yellow}) \)[/tex] in a simplified form. Since we have [tex]\( \frac{\overline{15}}{15} \)[/tex], this is equivalent to 1 (since any number divided by itself is 1).
Thus, we have:
[tex]\[ P(\text{not yellow}) = 1 \][/tex]
Since the probability of [tex]\( \text{not yellow} \)[/tex] is 1, the probability of its complement, which is the probability of yellow, would be:
[tex]\[ P(\text{yellow}) = 1 - P(\text{not yellow}) \][/tex]
[tex]\[ P(\text{yellow}) = 1 - 1 \][/tex]
[tex]\[ P(\text{yellow}) = 0 \][/tex]
So, the probability of yellow is 0.
Comparing this to the provided choices:
- [tex]\( P(\text{yellow}) = \frac{8}{15} \)[/tex]
- [tex]\( P(\text{yellow}) = \frac{11}{15} \)[/tex]
- [tex]\( P(\text{not yellow}) = \frac{8}{15} \)[/tex]
- [tex]\( P(\text{not yellow}) = \frac{11}{15} \)[/tex]
None of these choices directly state that [tex]\( P(\text{yellow}) = 0 \)[/tex]; however, based on the complementary relationship:
The correct understanding is [tex]\( P(\text{yellow}) = 0 \)[/tex] since [tex]\( P(\text{not yellow}) = 1 \)[/tex]. Therefore, none of the choices provided are correct based on the given information.
