Question

two balls are drawn from a bag containing 5 white and 7 black balls random
me probability that they would be of different colours.
1.
Two​

Answer 1

35/144+35/144

=70/144

Explanation:

assuming replacement of the first ball

P(white)=5/12

P(black)=7/12

P(white and black) =5/12×7/12

=35/144

P(black and white) =7/12×5/12=35/144

If the first ball is replaced:

P(different)=35/72

If the first ball is not replaced:

p(different)=35/66

Explanation:

There are 3 outcomes that can occur:

both are white both are blackone of each color

The probability of one of each color is 1−

P(same)

If the first ball is replaced:

P(WW)=5/12×5/12

=25/144

P(BB)=7/12×7/12

=49/144

∴

P(same)

=25/144+49/144

=74/144

P(different)=1−74/144

=70/144

=35/72

However, if the first ball is NOT replaced, the probability changes for the second ball. There are fewer of one color and one ball less.

P(WW)=5/12×4/11=20/132

P(BB)=7/12×6/11

=42/132

∴

P(same)

=20/132+42/132

=62/132

P(different)=1−62/132

=70/132

=35/66

I hope this is help you..