(a) Two a's and two b's are arranged in a specic order. All the possible random ar- rangements are equally likely. Given that the last letter, in order is b, nd the probability that two a's are next to each other. (Hint: Think about the sample space) (b) In a course 65% students are female and 35% students are male. The probability that a female student passes the course is 0.8 and the probability that a male student passes the course is 0.75. A student is randomly chosen from the class and found to have passed. What is the probability that the student is female