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. For each probability below, write your final answer as a rational number in lowest form. (a) If a randomly chosen student is asked two distinct randomly chosen questions from the test, what is the probability that the student will answer both questions correctly? 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. Find the probability that the chosen student was well prepared.
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.
For each probability below, write your final answer as a rational number in lowest form.
(a) If a randomly chosen student is asked two distinct randomly chosen questions from the test, what is the probability that the student will answer both questions correctly?
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. Find the probability that the chosen student was well prepared.