Question

In: Statistics and Probability

I have three urns, U1, U2 and U3, such the first urn contains w1 identical white...

I have three urns, U1, U2 and U3, such the first urn contains w1 identical white balls and b1 identical black balls, the second urn contains w2 identical white balls and b2 identical black balls, and the third urn contains w3 identical white balls and b3 identical black balls. I first choose a ball uniformly at random from U1 (i.e., every ball is equally likely to be picked) and drop it into U2. Next, I pick a ball uniformly at random from U2 and drop it into U3. Finally, I pick a ball uniformly at random from U3 and it turns out to be white. What is the probability that the ball that was transferred from U1 to U2 was black? Show the main steps of your solution.

Hint: Note that this problem is asking for a conditional probability. Use the tree method.

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orchestra answered 2 years ago
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