A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its colour is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marbles will be
(i) blue followed by red (ii) blue and red in any order (iii) of the same colour.
Number of blue balls = 3
Number of red balls = 5
Total number of balls = 3 + 5 = 8
(i) P(blue followed by red) = P (BR) = P(B) P(R)
(ii) P(blue and red in any order) = P (BR) + P (RB)
= P(B) P(R) + P(R) P(B)
(iii) P(of the same colour) = P(BB) + P(RR) = P(B) P(B) + P(R) P(R)
