A probability problem by Prosondip Sadhukan

Out of the 14 students taking a test, 5 are well prepared, 6 are adequately prepared and 3 are poorly prepared. There are 10 questions on the test paper. A well prepared student can answer 9 questions correctly, an adequately prepared student can answer 6 questions correctly and a poorly prepared student can answer only 3 questions correctly.

(a) If a randomly chosen student is asked two distinct randomly chosen questions from the test, let the probability that the student will answer both questions correctly be p(a).

Note: The student and the questions are chosen independently of each other. “Random” means that each individual student/each pair of questions is equally likely to be chosen.

(b) Now suppose that a student was chosen at random and asked two randomly chosen questions from the exam, and moreover did answer both questions correctly. let us cosider the probability of the chosen student was well prepared is p(b) .

then p(a)*p(b)=?