請教新pp一題

已找過題庫區了,但似乎沒找到,在這先請問大家了.謝謝

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 porobability that the marble chosen will be red greater than the probability that the marble chosen will be white?

(1) r/(b+w) > w/(b+r)

(2) b-w>r

答案為A

the porobability that the marble chosen will be red :r/(r+b+w)

the probability that the marble chosen will be white:w/(r+b+w)

the porobability that the marble chosen will be red greater than the probability that the marble chosen will be white:r/(r+b+w)>w/(r+b+w)

r/(b+w) > w/(b+r) 不等式两边为正数，两边都取倒数，不等式方向改变

=> (b+w)/r<(b+r)/w

=> (b+w)/r+1<(b+r)/w+1

=> (b+w+r)/r<(b+w+r)/w

不等式两边为正数，两边都取倒数，不等式方向改变

=> r/(r+b+w)>w/(r+b+w)

高手！