To find the probability of Niles walking Patches and then Spike, we need to consider the following:
- There are 6 dogs in total.
- The probability of Niles walking Patches first is 1/6, since there are 6 dogs to choose from.
- After walking Patches, there are now 5 dogs left (including Spike) for the next walk. The probability of walking Spike next is 1/5.
Now, we can calculate the combined probability of both events occurring (walking Patches and then walking Spike):
\[ P(\text{Patches first}) \times P(\text{Spike second}) = \left(\frac{1}{6}\right) \times \left(\frac{1}{5}\right) = \frac{1}{30} \]
However, this option does not appear among your provided responses.
The closest option by a misunderstanding or rephrasing might seem to revolve around choices involving "1 sixth times 1 fifth" or similar phrases.
The correct answer, based on probabilities, is:
- 1 sixth times 1 fifth, which mathematically represents \( \frac{1}{6} \times \frac{1}{5} \).
Choose that option if it appears (for example, "1 sixth times 1 fifth").