Question: Suppose we have a box containing $8$ apples and $4$ oranges and a second box containing $10$ apples and $2$ oranges. One of the boxes

Suppose we have a box containing $8$ apples and $4$ oranges and a second box containing $10$ apples and $2$ oranges. One of the boxes is chosen at random (with equal probability of choosing either box) and an item is selected from the box and found to be an apple. Use Bayes' rule to find the probability that the apple came from the first box.

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