Question
A magician hides a key under one of four overturned cups, and begins to shuffle the cups around the table. The magician is not particularly
A magician hides a key under one of four overturned cups, and begins to shuffle the cups around the table. The magician is not particularly skilled at shuffling, so your probability of keeping track of the cup containing the key is 0.65. In this case, you always select the correct cup and the magician is impressed. In the event that you do not keep track of the cup containing the key, you must pick a cup at random so that the probability you select the correct cup is 0.25. If you select the correct cup, what is the probability that you did so by keeping track of the cup?
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