Two balls are drawn from an urn containing 2 white, 3 red and 4 black balls one by one without replacement. What is the probability that at least one balls is red?
Let A be the event of not getting a red ball in first draw and B be the event of not getting a red ball in second draw. Then,
Required probability=Probability that at least one ball is red=1–probability that none is red
= 1 - P(A and B) = 1 - P (A ∩ B) = 1 - P(A) P(B/A)
Now, P(A) = Probability of not getting a red ball in first draw
P(A) = Probability of getting an other colour (white or black) ball in first draw
When another colour ball is drawn in first draw there are 5 other colour (white or black) balls and 3 red balls, out of which one other colour ball can be drawn in 5C1 ways.
Substituting these values in (i), we have Required probability
