A bag initially contains 1 red and 2 blue balls. An experiment consisting of selecting a ball at random, noting its color and replacing it together with an additional ball of the same colour. If three such trials are made, then

Options

A. probability that at least one blue balls is drawn is `0.9`
B. probability that exactly one blue all is drawn is `0.2`
C. probability that all the drawn balls are red given that all the drawn balls are of same color is `0.2`
D. probability that at least one red ball is drawn is `0.6`

Answer

A, B, C, D

Explanation

(1) `P(E_(1))=1-P(R R R)=1-[(1)/(3)xx(2)/(4)xx(3)/(5)]=0.9`
(2) `P(E_(2))=3P(B R R)=3xx(3)/(2)xx(1)/(4)xx(2)/(5)=0.2`
(3) `P(E_(3))=P(R R R //(R R RuuBBB))`
`=(0.1)/(0.1+2/3xx3/4xx4/5)`
`=(0.1)/(0.1+0.4)=0.2`
(4) `P(E_(4))=1-P(BBB)=1-2/5=0.6`