Question

Charles is answering a multiple-choice quiz question and has to choose one of five answers, only one of which is correct. The sample space is Ω-fall possible answers) Let: K be the event that he knows the correct answer and C be the event that he selects the correct answer Furthermore we will assume that if he knows the correct answer he will definitely select the correct answer. If he does not know the correct answer he will guess by randomly picking one answer. Note: To gain full marks you must express the required probabilities in terms of these events as well as giving the correct numerical answer (a) If he knows the correct answer what is the probability that he will get the answer correct? b) If he does not know the correct answer what is the probability that he will get the answer (c) Suppose that Charles has not done much work and that P(K)-0.3. If he gets the (d) Compare your answer to (c) with P(K), which probability is larger? Explain why this (e) Let P(K)-k> 0 and assume that the question has n equally likely options (n > 1) correct? question correct what is the probability that he knew the right answer? makes intuitive sense. State P (C | Kc) and show that P (K | C) 〉 k. When (if ever) does P (K | C) = k? Hint: consider P KIC-)

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