Consider the probabilities calculated in the questions 1 through 3. Classify each of these probabilities as approximate, exact, probability could not be calculated or other (after ignoring rounding issues). The probability calculated in Question 1 is  Answer 1 Question 4The probability calculated in Question 2 isAnswer 2 Question 4The probability calculated in Question 3 is Answer 3 Question 4

(a) [4 marks] A student answers a multiple-choice examination question that offersfour possible answers. Suppose that the probability that he knows the answer tothe question is 0.8 and the probability that he guesses is 0.2. Assume that if thestudent guesses, the probability of selecting the correct answer is 0.25. If the studentcorrectly answers a question, find the probability that he really knew the correctanswer.(b) [5 marks] Suppose the student takes an examination with 3 multiple choice ques-tions. Let X denote the number of questions he gets correct. Assuming that thestudent answers each question independently, determine the probability distributionof X and calculate the expected value of X.(c) [10 marks] Suppose the student takes an examination with 2 multiple choice ques-tions. But this time, he gains confidence every time he knows the answer to a ques-tion. Specifically, if he knows the answer to the current question, then for the nextquestion the probability that he knows the answer becomes 0.9 and the probabilitythat he guesses becomes 0.1. If he does not know the answer to the current ques-tion, then for the next question the probability that he knows the answer and theprobability that he guesses remain 0.8 and 0.2, respectively. Again letting X denotethe number of questions he gets correct, determine the probability distribution of Xand calculate the expected value of X. We can assume the probabilities of knowingthe answer and guessing for the first question are 0.8 and 0.2, respectively.

A student attempts a test with 10 multiple-choice questions, where each question has 4 possible options. She does not know the correct answer to any of the questions and randomly selects one of the 4 options for each of them. What is the probability that she will get 3 questions correct?10C3(1/4)1010C3(3/4)3(1/4)710C3(1/4)3(3/4)7Binomial probability cannot be used here.

A True/False quiz has three questions. When guessing, the probability of getting a question correct is the same as the probability of getting a question wrong. What is the probability that a student that guesses gets at least 2 questions correct? (Give your answer to 2 decimal places)

Q18. The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is 1/4.Given that the student has answered the question correctly, the conditional probability that the student knows the correct answer is*2/33/45/68/9

A student answers a multiple-choice examination question that offersfour possible answers. Suppose that the probability that he knows the answer tothe question is 0.8 and the probability that he guesses is 0.2. Assume that if thestudent guesses, the probability of selecting the correct answer is 0.25. If the studentcorrectly answers a question, find the probability that he really knew the correctanswer