Question

A bag contains 5 black & 6 white balls. If two

balls are drawn together at random, then the

probability that these being of different colour-

Answer 1

Black balls = 5
white balls = 6
two balls are drawn together from bag . And we have to find probability that these being different colors.

Actually, here three cases are possible :
1. Both the balls are black
2. Both the balls are white
3. both the balls are different colors .
∴ P(different colors) = 1 - P(same colors )

If both balls are black
∴ P( BB) = 5/11 × 5/11 = 25/121 [ actually, probability for each ball = 5/11 so, probability for both balls = 5/11 × 5/11]

similarly, if both balls are white ,
∴ P(WW) = 6/11 × 6/11 = 36/121

∴ P(same colors ) = P(BB) + P(WW) = 25/121 + 36/121 = 61/121
Now, probability of different colors , P(different colors) = 1- P(same colors)
P(different colors ) = 1 - 61/121 = 60/121

Hence, probability of different colors = 60/121


Hope this helps:)