In a recent year, there were 18,187 U.S. allopathic medical school seniors who applied to residency programs and submitted their residency program choices. Of these seniors, 17,057 were matched with residency positions, with about 79.2% getting one of their top three choices. Medical students rank the residency programs in their order of preference, and program directors in the United States rank the students. The term “match” refers to the process whereby a student’s preference list and a program director’s preference list overlap, resulting in the placement of the student in a residency position.

1. Find the probability that a randomly selected senior was matched with a residency position and it was one of the senior’s top three choices.
2. Find the probability that a randomly selected senior who was matched with a residency position did not get matched with one of the senior’s top three choices.
3. Would it be unusual for a randomly selected senior to be matched with a residency position and that it was one of the senior’s top three choices?