A bag contains 4 balls, 2 red, 1 white and 1 black. A man draws two balls from the
bag and announces that one of the ball drawn is red.
What is the chance that the other ball drawn is also red?
Answer
One-third might seem to be the answer but it is incorrect. The question that should
be asked is: What is the chance of both balls drawn being red among all possible outcomes in
which at least one of the balls drawn is red?
Both balls are red : 2/4 x 1/3 = 1/6
At least one of the balls drawn is red : 1 - none of the balls drawn is red
= 1 - 2/4 x 1/3 = 5/6
Probability that the other ball is red: (1/6) / (5/6) = 1/5
