There are two groups of students. The first consists of ten males and eleven females; the second consists of five males and six females. Two representatives, one from each group, were chosen at random. After that, one more student was chosen for another job at random from the whole group of the thirty students remaining.

(a) Find the probability that the last student chosen is a female.

(b) Given that the last student chosen is a female, find the probability that the first two students chosen are also females.