Three bags contain a number of red and white balls as follows:
Bag 1 : 3 red balls, Bag 2 : 2 red balls and 1 white ball
Bag 3 : 3 white balls.
The probability that bag i will be chosen and a ball is selected from it is i/6, i = 1, 2, 3. What is the probability that
(i) a red ball will be selected?
(ii) a white ball is selected?
Bag 1 : 3 red balls,
Bag 2 : 2 red balls and 1 white ball
Bag 3 : 3 white balls
Now, let E1, E2 and E3 be the events of choosing Bag 1, Bag 2 and Bag 3 respectively and a ball is drawn from it.
And, we have
P(E1) = 1/6, P(E2) = 2/6 and P(E3) = 3/6
Therefore, the required probabilities are 7/18 and 11/18.