Probability

Question

The probability of a student passing an exam is 0.1. What is the probability that he passes the exam in the 3rd attempt? Please explain in details. I am confused about these two approaches:

Approach 1:
P(passing in 3rd attempt)=P(failed in 1st)*P(failed in 2nd)*P(passed in 3rd attempt)= (0.9)*(0.9)*(0.1) = 0.081

Approach 2:
The pass rate will always remain constant no matter on which attempt he is trying. ie. Answer = 0.1
  

Which one is wrong and why?

Answer 1

It should be the first approach.

You are correct about the fact that the pass rate will remain the same, no matter what the attempt is. However, the question doesn't ask that. If the question was "What is the probability of him passing in the third exam?. For this, the answer would be 0.1, as you've written.

Here, the question implies that he failed in the first two exams and passed in the third. Hence, the answer is 0.9 x 0.9 x 0.1