Niles has 6 dogs. He can only walk them 1 at a time. What is the probability of Niles walking Patches and then walking Spike?

Answer 1

To determine the probability of Niles walking Patches and then Spike, we can use the concept of conditional probability.

1. Total number of dogs: Niles has 6 dogs.
2. Probability of walking Patches first: The probability that Niles chooses Patches first is \( \frac{1}{6} \), since there are 6 dogs.

Once Patches has been walked, there are now 5 dogs remaining.

3. Probability of walking Spike next: The probability that Niles then chooses Spike from the remaining 5 dogs is \( \frac{1}{5} \).

Now, we multiply these probabilities together to find the probability of both events happening in sequence (walking Patches first and then Spike):

\[ P(\text{Patches first, then Spike}) = P(\text{Patches first}) \times P(\text{Spike second | Patches first}) \] \[ P(\text{Patches first, then Spike}) = \frac{1}{6} \times \frac{1}{5} = \frac{1}{30} \]

Thus, the probability of Niles walking Patches and then walking Spike is \( \frac{1}{30} \).