A bag contains four red counters, three blue counters and three green counters. A counter is drawn at random from the bag and not replaced. A second counter is then drawn at random from the bag. Assuming that at each stage each counter left in the bag has an equal chance of being drawn,

(a) find the probability, giving your answers as fractions in their lowest terms, that the second counter will be blue given that (i) the first counter is red, (ii) the first counter is blue, (iii) the first counter is green.

(b) Find the probability, giving your answer as a fraction in its lowest terms, that the first counter will be red and the second counter. will be blue.

(c) Find the probability, giving your answer as a fraction in its lowest terms, that the second counter will be blue regardless of the colour of the first counter.