5. A box contains 2 identical pistols. Pistol A contains 7 live bullets and 3 blank bullets while pistol B contains 2 live bullets and 8 blanks. Following an annoying question from Holmes in his Stat 230 class, evil Professor Moriarty chooses a pistol at random and then fires once directly at Holmes. (Note: bullets are, of course, without replacement) (a) Find the probability that Holmes survives this shot (i.e. a blank bullet is fired). (b) If Holmes survives, he takes the other pistol and fires directly Moriarty. What is the probability that Holmes survives the first shot and Moriarty survives this second shot? (i.e. a both bullets fired are blank bullets.). (c) If this ill-considered game (do not play this game at home) continues until one of the two is shot with a live bullet, what is the probability that the person who survives is Holmes? (Note: Homes and Moriarty each retain the same pistol throughout)