2. A student is faced with a two-question exam. Unlike other exams, this particular exam has to be completed in order. As a result, a certain student believes that if they get a question correct, the probability of answering the next question correct increases by 0.05. However, if the student believes they incorrectly answer a question the probability of answering the next question correctly will decrease by 0.05. The probability of the student answering Question 1 correct is 0.60. To make marking simple both questions are worth only 1 mark each and there are no parts marks awarded. Let X be the number of total marks received for the two questions. Let U be the number of total marks received for question 1. Let W be the number of total marks received for question 2. Here are some partially completed probability tables use them only if they help (they are not for marks) X =x 0 1 2 P(X) = x shadle = 0.18 Contingency table of U =0 U =1 intersecting probabilities W = 0 0.18 W =1 0.4 0.6 1 a) What is the probability that this student got both questions correct? If rounding use at least 4 digits after the decimal [1] Answer. b) Find the covariance between Uand W, cov(U, W). If rounding use at least 4 digits after the decimal [1] Answer: c) Are Uand W independent random variables? Circle one: [1] Yes No If the student knows they did not get the second question correct, then what is the probability they scored a total of 1 mark on the exam? If rounding use at least 4 digits after the decimal [1]