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. 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)].
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?