Re: A box contains white marbles and black marbles, all identical except f
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25 Oct 2021, 13:56
The minimum number of marbles in the box is 8 (7 of which are white). If we increase the number of marbles by 6, we have 13 white marbles and 14 total marbles, so the new probability is 13/14 < 14/15. In the general case, we have 7*N white marbles and 8*N total marbles to start, and 7*N + 6/8*N+6 after adding the 6 white marbles. To prove the general case, let 7N + 6/8N+6 <14/15, then
(7N+6)*15 < (8N+6)*14,
105N + 90 < 112N + 84,
-7N < -6,
N > 6/7,
which must be true since N is a positive integer. Therefore the correct answer is B