Given that one urn contains two black balls and one white ball
and second urn contains one black ball and two white balls
It is also given that one of the two urns is chosen, then a ball is randomly chosen from the urn, then second ball is chosen at random from the same urn without replacing the first ball
(a) Sample Space S = {B1B2, B1W, B2W, B2B1, WB1, WB2, W1W2, W1B, W2B, W2W1, BW1, BW2}
Total number of sample space = 12
(b) If two black balls are chosen
Total outcomes = 12
Favourable outcomes are B1B2, B2B1
∴ Total favourable outcomes = 2
We know that,
(c) If two balls of opposite colours are chosen
Favourable outcomes are B1W, B2W, WB1, WB2, W1B, W2B, BW1, BW2
∴ Total favourable outcomes = 8
and Total outcomes = 12
We know that,