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There are three boxes. B1, B2, B3 The probability of selecting them is 0.2, 0.2 , 0.6 respectively.

B1 contains 3 red balls and 7 green balls. B2 contains 5 red balls and 5 green balls. B3 contains 2 red balls and 8 green balls.

If we select a box and then a ball from the box what is the probability that the ball is of red color.

If we select the a ball and it turns out to be of green color what is the probability that it comes from B3 ?

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closed as too localized by Qiaochu Yuan, Robin Chapman, Yemon Choi, Victor Protsak, Harry Gindi Aug 21 '10 at 7:06

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

MO is not really for such questions; have you read the FAQ? – Qiaochu Yuan Aug 21 '10 at 6:36
up vote 0 down vote accepted

Well, this looks more like someone trying to get their homework done, but for the first part:

$ p = 0.2 * \frac{3}{3+7} + 0.2 * \frac{5}{5+5} + 0.6 * \frac{2}{2+8}$

$ p = 0.06 + 0.10 + 0.12 $

$ p = 0.28 $

Showed the work for you too.

So if the probability that a chosen ball is red is 28%, then the probability that a chosen ball is green is 72%.

So what is {probability that chosen ball came from B3 | chosen ball is green}? Look up conditional probability, look up bayesian, etc.

$ p_g = 0.2 * \frac{7}{3+7} + 0.2 * \frac{5}{5+5} + 0.6 * \frac{8}{2+8}$

$ p_g = 0.14 + 0.10 + 0.48 $

$ p_g = 0.72 $

{ $p_g3$ | green ball} = (picked from box 3 and green) / (picked green)

= 0.48 / 0.72

= 2 /3

Please do your homework yourself. Showed the work for you too.

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Oh no the problem I am solving is entirely different. Just wanted to check that my line of thinking is correct. – Akshar Prabhu Desai Aug 21 '10 at 6:50
-1 : as a matter of policy, if you think that something is homework then you shouldn't answer it. – Andy Putman Aug 21 '10 at 14:54
Andy, I'm sorry that I didn't know about the restriction on what to answer. Should I edit the answer away? – sleepless in beantown Aug 22 '10 at 0:01
@sleepless : At this point, editing it is kind of pointless. Just keep it in mind in the future (I certainly understand the urge to answer questions even if they seem too easy!). – Andy Putman Aug 24 '10 at 2:08

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