大门|大门-CS-2005 |问题51

P区有2个红球和3个蓝球，Q区有3个红球和1个蓝球。将按如下方式选择一个球：

(i)  Select a box
(ii) Choose a ball from the selected box such that each ball in
     the box is equally likely to be chosen. The probabilities of
     selecting boxes P and Q are (1/3) and (2/3), respectively.  

假设在上述过程中选择的球是红色的球，那么它来自方框P的概率为 （A） 4/19 （B） 5/19 （C） 2/9 （D） 19/30 答复: （A） 说明：

The probability of selecting a red ball  = 
              (1/3) * (2/5) + (2/3) * (3/4) = 2/15 + 1/2 
              = 19/30  [Let it be P1]

Probability of selecting a red ball from box P =
             (1/3) * (2/5) = 2/15 [Let it be P2]

Given that a ball selected in the above process is 
a red ball, the probability that it came from the 
box P is = P1/P2 = (2/15) / (19/30) = 4/19 

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