📜  门| GATE-CS-2005 |第 51 题

📅  最后修改于: 2021-09-27 05:44:48             🧑  作者: Mango

盒子P有2个红球和3个蓝球,盒子Q有3个红球和1个蓝球。一个球的选择如下:

(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.  

给定上面过程中选择的一个球是一个红球,它来自盒子 P 的概率为
(一) 4/19
(乙) 5/19
(C) 2/9
(四) 19/30答案:(一)
解释:

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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