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
Answers
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