## Question

In a hurdle race, a runner has probability p of jumping over a specific hurdle. Given that in 5 trials, the runner succeeded 3 times, the conditional probability that the runner had succeeded in the first trial is

### Solution

3/5

Let A denote the event that the runner succeeds exactly 3 times out of five and B denote the event that the runner succeeds on th first trial.

But *P*(*B* ∩ *A*) = *P* (succeeding in the first trial and exactly once in two other trials)

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