Answer to Question #70777 in Statistics and Probability for monika

Question

A student is appearing in 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. The marking on the ball will determine her answer to the question. She randomly selects one ball for each question and replaces the ball in the box. There are five multiple-choice questions on the exam.
vi) Find sample space of the correct answers.
vii) If X represents the numbers of correct answers, then find the probability distribution of X.
viii) Find the distribution function of the random variable X and draw its graph.
ix) What is the probability that she will get more than four questions correct?
x) What is the probability that she will get no more than two questions correct?
xi) If each question is of 2 marks, what is the expected value of the correct answers?