Discrete Mathematics
# Discrete Probability

There are 100 people in line to board a plane with 100 seats. The first person has lost his boarding pass, so he takes a random seat.

Everyone that follows takes their assigned seat if it's available, but otherwise takes a random unoccupied seat. What is the probability the last passenger ends up in his/her assigned seat, as a decimal?

**inside** the hexagon at 1 point?

Two players, Nihar and I, are playing a game in which we alternate tossing a fair coin and the first player to get a head wins. Given that I toss first, the probability that Nihar wins the game is \(\dfrac{\alpha}{\beta}\), where \(\alpha\) and \(\beta\) are coprime positive integers.

Find \(\alpha + \beta\).

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