Question

Today, you want to go on a run. The probability of the day being windy is 52%. The probability of going for a run when it is windy is 23%. What is the probability of going on a run, given that it is a windy day?

Answer 1

To find the probability of going on a run given that it is a windy day, we need to clarify the terms involved:

- Let \( W \) be the event that it is windy.
- Let \( R \) be the event that you go for a run.

We are given:
- The probability of it being windy \( P(W) = 0.52 \).
- The probability of going for a run given that it is windy \( P(R | W) = 0.23 \).

The probability \( P(R | W) \) is the probability of going for a run given that the day is windy.

Even though the question mentions "the probability of going on a run when it is windy", it already gives us that probability: \( P(R | W) = 0.23 \).

Thus, the probability of going on a run, given that it is a windy day, is:

\[
P(R | W) = 0.23
\]

So the answer is **23%**.