# Probability of choosing a white ball from one of two random bags [closed]

One bag contains $4$ white balls and $2$ black balls and a second bag contains $3$ of each color. A bag is selected at random and a ball is drawn at random from the chosen bag. What is the probability that the ball chosen is white?

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## closed as not constructive by Andres Caicedo, Amzoti, Stefan Hansen, Julian Kuelshammer, Davide GiraudoMay 5 '13 at 9:11

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A question is chosen uniformly at random from the questions asked on math.SE today. What is the probability that it will not include any efforts at a solution? –  joriki May 5 '13 at 5:35
@joriki What have you tried? –  k.stm May 5 '13 at 5:39
The reason given for closure is manifestly false. –  Brian M. Scott May 5 '13 at 13:33
@TMM: The reason given is still rubbish. And I really don’t care that the user simply copied the question, especially since this was the user’s first question. –  Brian M. Scott May 5 '13 at 15:01
@TMM: I don’t actually care much about this particular question, since it has two adequate answers. But on principle I intend to nominate for re-opening every genuinely mathematical question that I see has been closed for what I consider inadequate or unacceptable reason. –  Brian M. Scott May 5 '13 at 17:26

$$\frac{1}{2}\Big(P[\text{white in 1st bag}] + P[\text{white in 2nd bag}]\Big).$$ Next time describe your attempt, else you will rarely get any reply (with such easy questions).
I believe this is just an application of the law of total probability. That is $$P(B=W)=P(B=W|Bag1)P(Bag1)+P(B=W|Bag2)P(Bag2)$$ where P(Bag1), P(Bag2) denote the probability that bag1, bag 2 is chosen and P(B=W) is the probability that the ball is white. I'll let you compute the probabilities and plug it into the formula.