# 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

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

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

## 2 Answers

$$\frac{1}{2}\Big(P[\text{white in 1st bag}] + P[\text{white in 2nd bag}]\Big).$$ Next time describe your attempt, else you will rarely get any reply (with such easy questions).

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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.

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