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In the experiment of rolling two fair dice successively, what is the probability that a sum of 5 appears before a sum of 7? Hint: See Exercise 36.
Exercise 36:
Let S be the sample space of a repeatable experiment. Let A and B be mutually exclusive events of S. Prove that, in independent trials of this experiment, the event A occurs before the event B with probability P (A)/[P (A) + P (B)]. Hint: See Example 3.31; this exercise can be done the same way.
Example 3.31
We draw cards, one at a time, at random and successively from an ordinary deck of 52 cards with replacement. What is the probability that an ace appears before a face card?
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