Question

A bag contains 5 black and 6 white balls . If two balls are drawn together at random then the probability the this being off different colour is

Answer 1

A bag contains 5 black balls and 6 white balls. Two balls are chosen at random. What is the probability that the chosen balls are of different colours?

Black balls = 5

White Balls=6

Total balls=11.

Number of ways of choosing 2 balls = 11c2=55.

Now,Probability that both balls are of different colour =1 -Prob. That both are of same color.

So we find the probability that both the balls are of same color =

(5c2 +6c2)/11c2

=25/55

=5/11.

So required Probability= 1–5/11

=6/11.

Alternative way:

For probability that both balls are of different colour you have to choose two diff coloured balls.

Let first ball choosen be red and other be white.

So Required Probability is :

(5c1×6c1)/11c2

30/55

=6/11.

Hope This helps

:)