A student failed two exams He can retake the rst one and he

A student failed two exams. He can retake the rst one and he will pass withprobability p. He can also retake the second exam and pass with probabilityq, but he must rst pass the rst exam. All trials are independent. Weknow that after 15 trials he did not yet pass the second exam. What is thechance that he did not pass the rst either?

Solution

As each trial is independent, so the probability of not passing the second exam as well as the first exam after 15 trials will be the multiplication of the individual probability of not passing the second exam as well as the second exam in all 15 trials.

so, the required probability = (1-p)¹⁵(1-q)¹⁵