2. [10 pts] Alice conducts in private the following experiment. First she flips a fair coin....

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2. [10 pts] Alice conducts in private the following experiment. First she flips a fair coin. If the coin comes up heads she (independently) rolls a fair die once. If the coin comes up tails she rolls a fair die turice, independently, and independently of the coin flip. Alice does not tell Bob what the coin showed but she tells Bob a number that she obtains as follows: . If she rolled the die once she just tells Bob what number the die showed. . If she rolled the die tuice she adds the two numbers shown and tells Bob that sum. (a) [5 pts] Calculate the probability that Alice tells the number 6 to Bob. (b) [5 pts] Suppose Alice tells Bob the number 6. What seems more likely to Bob: that the coin came up heads or that it came up tails? Remember to describe the probability space and to justify your answers. Solution. (a) YOUR SOLUTION TO PART (a) HERE (b) YOUR SOLUTION TO PART (b) HERE 2. [10 pts] Alice conducts in private the following experiment. First she flips a fair coin. If the coin comes up heads she (independently) rolls a fair die once. If the coin comes up tails she rolls a fair die turice, independently, and independently of the coin flip. Alice does not tell Bob what the coin showed but she tells Bob a number that she obtains as follows: . If she rolled the die once she just tells Bob what number the die showed. . If she rolled the die tuice she adds the two numbers shown and tells Bob that sum. (a) [5 pts] Calculate the probability that Alice tells the number 6 to Bob. (b) [5 pts] Suppose Alice tells Bob the number 6. What seems more likely to Bob: that the coin came up heads or that it came up tails? Remember to describe the probability space and to justify your answers. Solution. (a) YOUR SOLUTION TO PART (a) HERE (b) YOUR SOLUTION TO PART (b) HERE