To find the experimental probability that the next person to sign up for the genetics lecture will have hazel eyes, we can use the following formula for probability:
\[ P(\text{hazel}) = \frac{\text{Number of people with hazel eyes}}{\text{Total number of people signed up}} \]
In this case, the number of people with hazel eyes is 8, and the total number of people signed up is 18. Therefore, we can substitute in these values:
\[ P(\text{hazel}) = \frac{8}{18} \]
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ P(\text{hazel}) = \frac{8 \div 2}{18 \div 2} = \frac{4}{9} \]
So, the experimental probability that the next person to sign up will have hazel eyes is:
\[ P(\text{hazel}) = \frac{4}{9} \]