Answer: 48/91
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Work Shown:
We have 8 red and 6 white giving 8+6 = 14 total
The probability of selecting red is 8/14.
After that ball is not replaced, we have 14-1 = 13 balls left. The number of white balls will not go down since only the red ball count goes down.
The probability of selecting white on the second selection is 6/13
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So we can say
P(red first, then white) = P(red first)*(white second, given red first)
P(red first, then white) = (8/14)*(6/13)
P(red first, then white) = (8*6)/(14*13)
P(red first, then white) = 48/182
P(red first, then white) = 24/91
Let's label this as A.
A = 24/91
That way we can come back to it later.
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Now let's say we pick white first, then red
So we'd have the following.
P(white first, then red) = P(white first)*(red second, given white first)
P(white first, then red) = (6/14)*(8/13)
P(white first, then red) = (6*8)/(14*13)
P(white first, then red) = 48/182
P(white first, then red) = 24/91
Let B = 24/91
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Now we add up the values of A and B
A+B = 24/91 + 24/91
A+B = (24+24)/91
A+B = 48/91