To find the probability that someone's favorite activity is sleeping, we first note the total number of respondents and the activities they favored.
Out of 150 respondents:
- 30 favored building a snowman
- 80 liked skiing
- 40 preferred sledding
To determine the number of respondents who didn't favor any of these listed activities, we sum the number of respondents who favored the specified activities:
\[ 30 + 80 + 40 = 150 \]
Since all 150 respondents selected one of the activities listed, it implies that no respondents mentioned sleeping as their favorite activity.
Given that 0 respondents favored sleeping, the probability of selecting someone whose favorite activity is sleeping is:
\[ \text{Probability} = \frac{\text{Number of respondents who favor sleeping}}{\text{Total number of respondents}} = \frac{0}{150} = 0 \]
Therefore, the experimental probability that someone's favorite activity is sleeping is:
\[ \boxed{0} \]