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题库 / Prep2007E2-DS-152
A certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
(1) ~$\frac{r}{b+w}> \frac{w}{b+r}$~
(2) b – w > r
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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(1)b(r-w)+(r^2-w^2)>0-->b(r-w)+(r+w)(r-w)>0-->(r-w)(r+w+b)>0,因为r,b,w表示个数，都是正整数，所以r>w。
通常情况下，2个分数分子分母各自一小一大是无法比较大小的，分子分母都是正数的情况。如：
a,A都是正数，已知A/a>a/A,问是否A>a?
-->(A^2-a^2)/(a*A)>0,因为a,A都是正数，所以A^2>a^2,-->A>a
求：r / (b+w+r) > w / (b+w+r) => rb+rw+rr > wb+ww+wr => rb+rr > wb+ww
A: r / (b+w) > w / (b+r) => rb+rr > wb+ww (正确）
rb+wb>ww-rr
(r-w)*b+w+r)>0
r-w>0