3. Suppose academic misconduct cases at a college are presented to a 3-person committee and a student receives a verdict of guilty if at least 2 committee members vote 'guilty'. If the student is guilty, then each committee member will independently vote 'not guilty' with probability 0.2. If the student is innocent, then each committee member will independently vote 'guilty' with probability 0.1. The probability that a student in an academic misconduct case is guilty is 0.65. [7 marks] (a) What is the probability that a committee member will vote 'guilty' in an academic misconduct case? (b) What is the probability that a student in an academic misconduct case receives a ver- dict of guilty