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A nationwide school examination in history included several multiple-choice questions. Each question had 4 possible answers,...
A student answers a multiple choice examination with questions that have four possible answers each. Suppose...
A student answers a multiple choice examination with questions that have four possible answers each. Suppose that the probability that the student knows the answer to a question is 0.80 and the probability that the student guesses is 0.20. If the student guesses, the probability of guessing the correct answer is 0.25. The questions are independent, that is, knowing the answer on one question is not influenced by the other question. (a) If there is one question on the exam...
Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a...
Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 65% chance of answering any question correctly. (Round your answers to two decimal places.) (a) A student must answer 43 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination?...
Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a...
Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 75% probability of answering any question correctly. A student must answer 43 or more questions correctly to obtain a grade What percentage of the students who have done their homework and attended lectures will obtain a grade A on this multiple-choice examination? A student who answers 35 to 39 questions correctly will receive...
(5 points) A multiple-choice examination has 15 questions, each with 5 possible answers only one ...
(5 points) A multiple-choice examination has 15 questions, each with 5 possible answers only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that the student answers at least four questions correctly? What is the expected number of questions that the student answers correctly? 4.
(5 points) A multiple-choice examination has 15 questions, each with 5 possible answers only one...
12. In an entrance examination with multiple choice questions, with each question having four options and...
12. In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only 20% candidates think they know the answer to one difficult question and only half of them know it correctly and the other half get it wrong. The remaining candidates pick one option out of the four randomly and tick the same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew...
7. In answering a question on a multiple-choice test, a student either knows the answer or...
7. In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let p be the probability that the student knows the answer and 1-p be the probability that the student guesses. Suppose there are 5 multiple-choice alternatives so a student who guesses at the answer will be correct with probability 1/5. (o) Show that the probability that a student knew the answer to a question given that he or she (b) What is the...
3. [10 Points! Consider an exam with multiple choice questions. Assume that each question has three...
3. [10 Points! Consider an exam with multiple choice questions. Assume that each question has three solution choices but only one of them is correct. A student who didn't study for the exam is going to make a guess. 3. What is the probability that he guesses only 15 questions correctly What is the probability that he guesses at least 15 questions correctly c. What is the probability that he guesses more than 10 and less than 15 questions correctly?...
A quiz consists of 6 multiple-choice questions. Each question has 4 possible answers. A student is...
A quiz consists of 6 multiple-choice questions. Each question has 4 possible answers. A student is unprepared, and he has no choice but to guess answers completely at random. He passes the quiz if he gets at least 3 questions correctly. What is the probability that he will pass?
3. [10 Points) Consider an exam with 28 multiple choice questions. Assume that each question has...
3. [10 Points) Consider an exam with 28 multiple choice questions. Assume that each question has three solution choices but only one of them is correct. A student who didn't study for the exam is going to make a guess. a. What is the probability that he guesses only 15 questions correctly? b. What is the probability that he guesses at least 15 questions correctly? c. What is the probability that he guesses more than 10 and less than 15...
5. A student takes a multiple-choice exam where each question has 5 possible answers. He works...
5. A student takes a multiple-choice exam where each question has 5 possible answers. He works a question correctly if he knows the answer, otherwise he guesses at random. Suppose he knows the answer to 80% of the questions. (a) What is the probability that on a question chosen at random the student gets the correct (b) Given that the student gets the correct answer to this question, what is the probability answer? that he actually knew the answer?
(5 points) A multiple-choice examination has 15 questions, each with 5 possible answers only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that the student answers at least four questions correctly? What is the expected number of questions that the student answers correctly? 4.
(5 points) A multiple-choice examination has 15 questions, each with 5 possible answers only one...
12. In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only 20% candidates think they know the answer to one difficult question and only half of them know it correctly and the other half get it wrong. The remaining candidates pick one option out of the four randomly and tick the same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew...
7. In answering a question on a multiple-choice test, a student either knows the answer or guesses. Let p be the probability that the student knows the answer and 1-p be the probability that the student guesses. Suppose there are 5 multiple-choice alternatives so a student who guesses at the answer will be correct with probability 1/5. (o) Show that the probability that a student knew the answer to a question given that he or she (b) What is the...
3. [10 Points! Consider an exam with multiple choice questions. Assume that each question has three solution choices but only one of them is correct. A student who didn't study for the exam is going to make a guess. 3. What is the probability that he guesses only 15 questions correctly What is the probability that he guesses at least 15 questions correctly c. What is the probability that he guesses more than 10 and less than 15 questions correctly?...
3. [10 Points) Consider an exam with 28 multiple choice questions. Assume that each question has three solution choices but only one of them is correct. A student who didn't study for the exam is going to make a guess. a. What is the probability that he guesses only 15 questions correctly? b. What is the probability that he guesses at least 15 questions correctly? c. What is the probability that he guesses more than 10 and less than 15...
5. A student takes a multiple-choice exam where each question has 5 possible answers. He works a question correctly if he knows the answer, otherwise he guesses at random. Suppose he knows the answer to 80% of the questions. (a) What is the probability that on a question chosen at random the student gets the correct (b) Given that the student gets the correct answer to this question, what is the probability answer? that he actually knew the answer?
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