Problem 5 (Bayes’ rule). A student is taking a multiple-choice exam in which each question has four possible answers. She knows the answers to 60% of the questions and guesses at the others. What is the probability that she guessed given that she guessed question 12 right?
P(correct answer)=P(knows and correct)+P(guessed and correct) =0.6*1+0.4*1/4=0.7
therefore P(guessed given correct )=P(guessed and correct)/P(correct)=0.4*(1/4)/0.7 =1/7 =0.1429
Problem 5 (Bayes’ rule). A student is taking a multiple-choice exam in which each question has...
A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A,B,C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five...
A student is taking a multiple-choice exam in which each question has two choices. Assuming that she has no knowledge of the correct answers to any of thequestions,she has decided on a strategy in which she will place two balls( marked (A and B) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are six multiple-choice questions on...
A student is taking a multiple-choice exam in which each question has four choices. Assume that the student has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There...
A student is taking a multiple-choice exam in which each question has two choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place two balls (marked Upper A and Upper BA and B) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question....
A student is taking a multiple-choice exam in which each question has five choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place five balls (marked Upper A comma Upper B comma Upper C comma Upper D comma and Upper E) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the...
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?
A student is taking a multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are...
3) Suppose a student is taking a multiple-choice question exam in which each answer has four choices. Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on the following strategy: She will place four balls marked A, B, C, and D in a box. She randomly selects one ball for each question and replaces the ball in the box after marking the letter of the ball as the answer. If there...
answer for d part A student is taking a multiple-choice exam in which each question has five choices Assuming that she has no knowledge of the correct answers to any of the questions, she has decided on a strategy in which she will place five balls (marked A, B, C, D, and E) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer...
Exercise 1.4. On a multiple-choice exam with four choices for each question, a student either knows the answer to a question or marks it at random. Suppose the student knows answers to 70% of the exam questions. If she marks the answer to question 1 correctly, what is the probability that she knows the answer to that question?