An urn contains 7 white, 5 black and 3 red balls.
Two balls are drawn at random. Find the probability
(i) both the balls are red
(ii) one ball is red, the other is black
(iii) one ball is white
Total number of balls in the urn = 7 + 5 + 3 =
Outof these 15 balls, two balls can be drawn in
(i) Let Abe the event that both
the balls drawn are red.
Now, there are 3 red balls out of which 2 red
balls can be drawn in ways.
Thus, P(A) =
(ii) Let Bbe the event that of
the two balls drawn, one is red and the other is black.
There are 3 red balls out of which one red ball
can be drawn in 3C1ways and there are 5 black balls
out of which one black ball can be drawn in 5C1ways.
Thus, P(B) =
(iii) Let C be the event that of
the two balls drawn, one is white.
There are 7 white balls and 8 non-white balls. Two
balls can be drawn out of them, one ball being white and the
other being non-white, in
Thus, P(C) =