To obtain a certain job a student must pass a certain exam T

To obtain a certain job, a student must pass a certain exam. The exam may be taken many times. If the student passes on the first try, she gets the job. If not, she still gets the job if at some times the number of passing attempts exceeds the number of failures by two. If at any time the number of failures exceeded the number of passes by two, she is not allowed to ever take the exam again. The probability of the student passing on each particular try is ½. What is the probability she gets a job.

Solution

What is the probability she gets a job.

1/2 * 1/2 / 2

0.125