Let’s assume that there are two dice, and we will roll one of them, but we don’t know which one. The probability of rolling either dice is 1/2. One of them is fair in the sense that all 6 outcomes are equally likely. The other die gives probability 1/3 to numbers 1 through 3 and zero probability to numbers 4-6.
a-)The first roll was a 4. What is the probability that it was the fair die?
b-)The first roll was a 3. What is the probability that it was the fair die?
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