Probability of getting two black balls: 4/8 x 3/7 = 12/56
Probability of getting the first ball to be black and the second ball to be white: 4/8 x 4/7 = 16/56
Now, put back the white ball and draw; the probability of getting a black ball on this draw is 3/7.
Final probability for this case: 16/56 x 3/7 = 48/392.
Probability of getting the first ball to be white and the second ball to be black: 4/8 x 4/7 = 16/56
Now, put back the white ball and draw; the probability of getting a black ball on this draw is 3/7.
Final probability for this case: 16/56 x 3/7 = 48/392.
Probability of getting two white balls: 4/8 x 3/7 = 12/56
Now, put back the two white balls and draw; the probability of getting two white balls: 4/8 x 3/7 = 12/56.
Final probability for this case: 12/56 x 12/56 = 144/3136.
To find the total probability, we need to add these answers: 12/56 + 48/392 + 48/392 + 144/3136 = 99/196.