一道Manhattanprep的Q题 感觉有些争议 求解

天山居士UID：3540709

Six billiard balls, numbered 1 through 6, are placed in a box. Three of the balls are red, and three are blue. One ball is to be drawn randomly from the box.

Quantity A
The probability that the ball drawn will be an even numbered red ball

Quantity B
1/2

1, Quantity A is greater.
2, Quantity B is greater.
3, The two quantities are equal.
4, The relationship cannot be determined from the information given.

在贴答案之前我想看看大家怎么approach这个题的，大谢！

logicallyUID：3447866

你是不是想说 题目没说清楚哪几号球是红色哪几号球是蓝色？
确实题目表述不清楚

天山居士UID：3540709

logically 发表于 2014-9-12 10:59
你是不是想说 题目没说清楚哪几号球是红色哪几号球是蓝色？
确实题目表述不清楚

考点就是不说清楚什么颜色对应什么数字，我不知道那样的话还能不能计算。假设题目是没问题的，就从数学来讲该怎么做？

贺小虎benUID：3494360

算了下，感觉A的概率应该是1/4?选B大吗

我是这么算的
下面的C3_6都是组合，就是6个里面选3个位置，实在不知道怎么表达上下标。。。
6个球，3红3蓝，填6个顺序的坑，C3_6*C3_3=20种情况
0个红在偶数坑，1种
1个红在偶数坑，C1_3*C2_3=9种
2个红在偶数坑，C2_3*C1_3=9种
3个红在偶数坑，1种

所以 取出偶数红球概率=1/20*0+9/20*1/6+9/20*2/6+1/20*3/6=1/4

如果有误或者有更简便的方法，请一定指出

hermione-yeahUID：2303422

我是这样想的，因为只是比大小。 从6个球里得到红球的概率是1/2, 奇偶未知， 想要得到偶数或奇数必然要再乘以这个条件的概率， 所以一定比0.5小啊。

天山居士UID：3540709

公布一下正确答案和答案解释吧：
The information given initially in this problem seems on first glance to be quite specific, but in reality says very little. No details are given regarding the distribution of the colors in terms of the numbers; it is possible that the even numbers are all red, or that none of them are. We are asked to compare the probability that the ball drawn will be even numbered and red with the value 1/2. If each even numbered ball happens to be red, then 3 of the 6 balls will satisfy this condition and the probability of drawing on of these balls will be 1/2. However, it is also possible that none of the even numbered balls is red (each could be blue), or perhaps only one or two. In these cases, the probability will be less than 1/2. Since we cannot determine which quantity is larger (either B is larger, or they are equal) the answer must be D.

The answer is D. (from ManhattanPrep)

hermione-yeahUID：2303422

谢谢解答，我忘了0.5*1的情况了

gksoUID：2188783

考虑极端情况就可以了，
3个红球都是偶数，3个篮球都是奇数。则抽到偶数红球的概率是1/2
其他情况概率都小于1/2，所以答案是不能确定到底相等还是小于