Suppose you are taking a test and the test has 12 multiple choice questions, eac
ID: 2958531 • Letter: S
Question
Suppose you are taking a test and the test has 12 multiple choice questions, each has 4 questions. To pass you must get 6 or more answers correct.a) What is the probability that you will get the first question correct?
b) What is the formula that will tell you your probability of getting exactly six correct?
c) What is the probability of getting exactly six correct?
d) Suppose the teacher decides to "grade on the curve" and passes anyone who gets at least four correct. What is the probability of passing?
Explanation / Answer
a) Let the letter "c" represent that you got the question correct and the letter "w" represent that you got the question wrong. In order to get 6 questions right on the 12 question test you should have a sequence that looks something like this. CCCCCCWWWWWW (6 c's and 6 w's). Except thats not the only way to get 6 questions right since the problem doesnt tell you which six. So you have to order the above sequence or "word" in some probability-speak. To arrange twelve letters there are (12!) (factorial notation) ways to do it. But the C's are identical and so are the W's. So to prevent overcounting you need to divide out the ways you can arrange the C's and W's. This gives: (12!)/(6!)(6!)=924 ways to arrange the word. There is a 1/4 chance you will get something right (4 multiple choice) and 3/4 that you will get something wrong. Plug these probabilities into each let where C = 1/4 and W = 3/4. Then multiply by the total arrangements for the probability. (1/4)^6 x (3/4)^6 x 924 = 0.040149 or around a 4% chance. b) Getting at least four correct is the same as the total probability minus getting 3, 2, and 1 correct. Everything left guarentees a pass. So repeat the same thing above: 3 correct: (12!)/(9!)(3!) = 220 220 x (1/4)^6 x (3/4)^6 = 0.009559 2 correct: (12!)/ (2!)(10!) = 33 33 x (1/4)^6 x (3/4)^6 =0.0014339 1 correct: (12!)/(11!)(1!)= 12 12 x (1/4)^6 x (3/4)^6 = 0.00052142 1-(0.009559)-(0.0014339)- (0.000521) = 0.98848 or there is a 98.8% chance that you will pass.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.