Answer to Question #286162 in Statistics and Probability for Navodya

Question

5. A person who wants to get a driving license, has to face two separate tests. Road test is the one of these two tests and there is a 0.75 probability that an application for a drivers license will pass the road test on any given try. 

i) What is the probability that an applicant will pass the road test on any given try? 

Answer 1

i) The probability that an applicant will pass the road test on any given try is $p=0.75.$

The probability that an applicant will finally pass the test on the $k$th try is

$$P(X=k)=p(1-p)^{k-1}, k=1, 2, ...$$