S The rencontre problem. Alice and Bob agree to play the following game: From two completely new, identical sets of playing cards, one is well shuffled. Both piles are put next to each other face down, and then revealed card by card simultaneously. Bob bets (for a stake of e 10) that in this procedure at least two identical cards will be revealed at the same time. Alice, however, is convinced that this is ‘completely unlikely’ and so bets the opposite way. Who do you think is more likely to win? Set up an appropriate model and calculate the probability of winning for Alice. Hint: Use Problem 1.7b; the sum that appears can be approximated by the corresponding infinite series.