请教新pp一题

bipedalisms

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

答案为A

poorleafs

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)

dingzhiyin19

高手！