Posted by vero on Monday, January 19, 2009 at 9:29pm.
The result of the second reach into the bag depends on the result of the first reach.
For example if the coach pulled a black one first, then for the second there would be 7 black and 7 red.
probability first one black = 8/15
then probability second one black = 7/14
so 8/15 * 7/14 for both black
probability first one not black = 7/15
probability second one not black = 6/14
so 7/15 * 6/14 for both white
add those two.
8/15 * 7/14 + 7/15 * 6/14
= (1/15)(56/14 + 42/14) = (1/15)(98/14)
= 98/210 = 49/105
Oh, 49/105 = 7/15
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