# 20 problems in probability

1Twenty problems in probabilityThis section is a selection of famous probability puzzles, job interview questions (most hightech companies ask their applicants math questions) and math competition problems. Someproblems are easy, some are very hard, but each is interesting in some way. Almost all problemsI have heard from other people or found elsewhere. I am acknowledging the source, or a partialsource, in square brackets, but it is not necessarily the original source.You should be reminded that all random choices (unless otherwise specified) are such thatall possibilities are equally likely, and different choices within the same context are by defaultindependent. Recall also that an even bet on the amount x on an event means a correct guesswins you x, while an incorrect guess means loss of the same amount.1. [P. Winkler] One hundred people line up to board an airplane. Each has a boarding pass withassigned seat. However, the first person to board has lost his boarding pass and takes a randomseat. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupiedseats at random otherwise. What is the probability that the last person to board gets to sit inhis assigned seat?2. [D. Knuth] Mr. Smith works on the 13th floor of a 15 floor building. The only elevatormoves continuously through floors 1, 2, . . . , 15, 14, . . . , 2, 1, 2, . . . , except that it stops on a flooron which the button has been pressed. Assume that time spent loa … Purchase document to see full attachment

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