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? (1 point) Responses 16⋅15 1 sixth times 1 fifth 16+15 1 sixth plus 1 fifth 16⋅16 1 sixth times 1 sixth 16 1 sixth

Answer 1

To solve the problem, we first need to understand the scenario.

Niles has 6 dogs and wants to walk Patches first and then Spike.

1. The probability of walking Patches first: Since there are 6 dogs to choose from, the probability of walking Patches first is \( \frac{1}{6} \).

2. After walking Patches, there are now 5 dogs left, including Spike. So, the probability of then walking Spike is \( \frac{1}{5} \).

3. To find the combined probability of both events (walking Patches first and then Spike), we multiply the two probabilities together:

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

Now, looking at the multiple choice responses provided, the correct way to express this probability is:

\[ \frac{1}{6} \times \frac{1}{5} \]

So, the correct answer is:

1 sixth times 1 fifth