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? (1 point) Consider the formula for conditional probability.

1 answer

To find the probability of going on a run given that it is a windy day, we can use the concept of conditional probability. Specifically, we can denote the events as follows:

  • Let \( A \) be the event that it is a windy day.
  • Let \( B \) be the event that you go for a run.

We are interested in finding \( P(B | A) \), which is the probability of event \( B \) given event \( A \).

According to the problem, we have:

  • \( P(A) = 0.52 \) (the probability of a windy day)
  • \( P(B | A) = 0.23 \) (the probability of going for a run when it is windy)

Since \( P(B | A) \) is already provided in the problem's context, it answers your question directly:

The probability of going on a run given that it is a windy day is \( 0.23 \) or 23%.