To find the experimental probability that the next man to walk by will have a beard, we can use the data that Lillian observed. The experimental probability \( P(\text{beard}) \) is calculated as the number of men with beards divided by the total number of men observed.
In this case, Lillian noticed that 3 out of the last 15 men had a beard. Therefore, we calculate:
\[ P(\text{beard}) = \frac{\text{Number of men with beards}}{\text{Total number of men observed}} = \frac{3}{15}. \]
Next, we simplify the fraction \( \frac{3}{15} \):
Both the numerator and the denominator can be divided by 3:
\[ \frac{3 \div 3}{15 \div 3} = \frac{1}{5}. \]
Thus, the experimental probability that the next man to walk by will have a beard is:
\[ P(\text{beard}) = \frac{1}{5}. \]