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A teacher is giving an exam where students will have to answer 6 essay questions. She gives the students 12 possible essay questions the week before the exam. A specific student, Bob, only has time to prepare for 8 of the questions.
a. Find the probability that bob has prepared for every essay on the test.
b. Find the probability that bob has prepared for exactly 3 of the essays on the test.
c. Find the probability that Bob has prepared for at least 1 of the essays on the test
1 Answer
- PaulaLv 76 years ago
I find it easier to think of it this way: Bob prepared 8 out of 12 questions, then the teacher chose 6 of them. Or: Bob put 8 red balls and 4 white balls in a bag, and the teacher took out 6 without replacement.
(c) is easy. Since Bob only omitted 4 questions, he had to be prepared for at least 2. So probability of being prepared for at least one test is 1. (i.e. it was certain).
For (a), just think of the teacher taking out one question (or ball) at a time as she chooses her 6.
p(teacher chose only questions bob had prepared)
= 8/12 x 7/11 x 6/10 x 5/9 x 4/8 x 3/7 (EDITED and corrected)
EDIT: OK for (b). First, think of the probability of choosing 3 revised questions then 3 non-revised questions:
p_partial = 8/12 x 7/11 x 6/10 (for the 3 revised questions) x 4/9 x 3/8 x 2/7 (for the 3 non-revised questions). But choosing 3 revised and 3 non-revised can be arranged in C(6,3) ways (6x5x4 / (3x2x1)) = 20, so you multiply the probability p_partial by that number, you should get about 0.24