The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. The range is the set of all valid y values.
P(Al hits bottle first time) = 1/3 P(Al misses the first shot but hits on his second shot) = P( Al misses and bill misses and Al hits) = 2/3 * 3/4 * 1/3 = 1/6