Question: 4. Suppose we have a multiple choice quiz with 10 questions, each of which has 4 options (of which only one is correct). Suppose I

4. Suppose we have a multiple choice quiz with 10 questions, each of which has 4 options (of which only one is correct). Suppose I answer each multiple choice question by completely guessing. Let X be the number of correct answers. 5 marks (a) State the distribution of X, with it's parameter(s). (b) Find the probability I get exactly 8 of the answers right. (c) Find the probability I pass the quiz if I only need 30% to pass. Now suppose instead that we have an infinite number of multiple choice questions in front of us, still with 4 possible answers of which only one was correct. Let Y be the question number in which I get my first correct answer. 5 marks (a) State the distribution of Y, with it's parameter(s). (b) Find the probability my first correct answer is on the 5th question. (c) Find the probability I got my first correct answer on my second go, given that I failed my first question.

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