Question
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?
Answers
GPT-4o mini
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 \( \frac{1}{30} \).
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 \( \frac{1}{30} \).