A bag initially contains one red ball and two blue balls. An experiment consists of selecting a ball at random, noting its colour and replacing it together with an additional ball of the same colour. If three such trials are made, then 

Probability that at least one blue ball is drawn = 1 - Probability that all the balls drawn are red. 

$=1-\frac{1}{3}.\frac{1}{2}.\frac{3}{5}=1-\frac{1}{10}=\frac{9}{10}=0.9$

Probability that exactly one blue ball is drawn $=\frac{1}{3}.\frac{1}{2}.\frac{2}{5}+\frac{2}{3}.\frac{1}{4}.\frac{2}{5}+\frac{1}{3}.\frac{2}{4}.\frac{2}{5}=0.2$

Probability that all drawn balls are red given that all the drawn balls of the same colour 

$=\frac{{\displaystyle \frac{1}{10}}}{{\displaystyle \frac{1}{10}}+{\displaystyle \frac{4}{10}}}=\frac{1}{5}=0.2$

Probability that at least one red ball is drawn $=1-\left(\frac{2}{3}.\frac{3}{4}.\frac{4}{5}\right)=0.6$