A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. Hint: Let&nbsp;En&nbsp;denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n-1 rolls. Compute&nbsp;P(En)&nbsp;and argue that&nbsp;∑n=1∞P(En)&nbsp;is the desired probability.

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A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probability that a 5 occurs first. Hint: Let&amp;nbsp;En&amp;nbsp;denote the event that a 5 occurs on the nth roll and no 5 or 7 occurs on the first n-1 rolls. Compute&amp;nbsp;P(En)&amp;nbsp;and argue that&amp;nbsp;∑n=1∞P(En)&amp;nbsp;is the desired probability.

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Experiment: Throwing two fair six sided dice.  Use the notation from the exercise:  En - Event that a sum of 5 is rolled in the n-th roll, and neither 5 or 7 were rolled before.  Now every event where the sum of 5 is rolled before 7 is some En - because the checking if this event happened in the experiment is: from the begging watch for sum of 5 or 7, if the sum of 5 appeared first both sums, lets say in n-th roll this is event En  We have 36 equally likely possibilities for every dice roll, this means a total of 36n possibilities.  4 of these 36−(1,4),(4,1),(2,3),(3,2) are possible if the sum is 5 and 6 are possible if the sum is 7.  This leaves 26 possible rolls that sum up to a number thats

A pair of dice is rolled until a sum of either 5 or 7 appears. Find the probabil

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