A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: B
Solution
P(red on 2nd draw) = P(1st red) × P(red | 1st red) + P(1st black) × P(red | 1st black).
If 1st ball is red (prob = 4/10): bag becomes 6 red + 6 black = 12 balls, so P(red) = 6/12 = 1/2.
If 1st ball is black (prob = 6/10): bag becomes 4 red + 8 black = 12 balls, so P(red) = 4/12 = 1/3.
Total = (4/10)(1/2) + (6/10)(1/3) = 2/10 + 2/10 = 4/10 = 2/5.
If 1st ball is red (prob = 4/10): bag becomes 6 red + 6 black = 12 balls, so P(red) = 6/12 = 1/2.
If 1st ball is black (prob = 6/10): bag becomes 4 red + 8 black = 12 balls, so P(red) = 4/12 = 1/3.
Total = (4/10)(1/2) + (6/10)(1/3) = 2/10 + 2/10 = 4/10 = 2/5.
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