The semester is over and at last Alice is back home for the summer break. Since...

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The semester is over and at last Alice is back home for the summer break. Since she has worked so hard throughout these past few months (as all of you have), her family decided to give her some rest while everybody else is busy preparing for their upcoming trip. The moment she lies down on the sofa something sharp pokes her head: a die. Due to boredom and the probabilistic reflexes she has recently developed, Alice starts to roll the die, at each roll recording the value that came up and adding it to the values already recorded. After Alice rolls the die many many times, what is the approximate probability that her number is divisible by 13? Justify your answer. The semester is over and at last Alice is back home for the summer break. Since she has worked so hard throughout these past few months (as all of you have), her family decided to give her some rest while everybody else is busy preparing for their upcoming trip. The moment she lies down on the sofa something sharp pokes her head: a die. Due to boredom and the probabilistic reflexes she has recently developed, Alice starts to roll the die, at each roll recording the value that came up and adding it to the values already recorded. After Alice rolls the die many many times, what is the approximate probability that her number is divisible by 13? Justify your answer.