There are 3 black and 4 white balls in a box. One ball is taken out...
Homework Answers
There are 3 black and 4 white balls in a box
P[ the ball in first draw is black ] = 3/7
P[ the ball in first draw is white ] = 4/7
Case 1 : If black ball was drawn in the first draw
If it is black, then two white balls are put back in the box
New composition : There are 3 black and 6 white balls in a box
P[ drawing white ball in second draw | first ball was black ] = 6/9 = 2/3
Case 2 : If white ball was drawn in the first draw
If it is white, then one black ball is put back in the box
New composition : There are 4 black and 4 white balls in a box
P[ drawing white ball in second draw | first ball was white ] = 4/8 = 1/2
P[ drawing white ball in second draw ] = P[ drawing white ball in second draw | first ball was white ]*P[ the ball in first draw is white ] + P[ drawing white ball in second draw | first ball was black ]*P[ the ball in first draw is black ]
P[ drawing white ball in second draw ] = (4/7)(1/2) + (3/7)(2/3)
P[ drawing white ball in second draw ] = 2/7 + 2/7
P[ drawing white ball in second draw ] = 4/7
P[ both balls are white ] = P[ the ball in first draw is white ]*P[ drawing white ball in second draw ]
P[ both balls are white ] = (4/7)(4/7)
P[ both balls are white ] = 16/49
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