In Monopoly, your token is allowed to leave the ”jail” cell if you roll doubles: you roll two 6 -sided dice and each shows the same face. Zach hates being in jail, So he invents a couple of weighted dice that are not independent. In particular, if you roll either die on its own it’s a fair die: each outcome has probability 1/6. But if you roll one die and then the other, the red die will take the same outcome as the blue die exactly half the time: all other outcomes are equally likely. (a) Suppose you roll a 3 on the blue die. What is the probability distribution of the red die given this outcome on the blue die? (b) What is the probability you roll doubles? (c) What is the probability that you roll a 7 as the sum of the two dice?
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distribution of the red if you roll a 3 on the blue die:
the probability you roll doubles is 1/2
probability that you roll a 7 as the sum of the two dice: