induction

Discovering the Minimum Pairwise Correlation: X, Y, Z

atypicalquant
July 25, 2022January 4, 2024

X, Y, and Z are three random variables with mutual pairwise correlation rho. What is the minimum possible value that rho can take?

Read More »Discovering the Minimum Pairwise Correlation: X, Y, Z

Plane Boarding Puzzle: Will the Last Person Get Their Seat?

atypicalquant
February 7, 2022January 4, 2024

There are 100 people in line to board a plane that seats all of them. The first person in line is drunk and decides to take a random seat. Every person that boards the plane after them will either: take the seat on their ticket or if that seat is taken, a random one instead.

What is the probability that the last person that boards will end up in their assigned seat?

Read More »Plane Boarding Puzzle: Will the Last Person Get Their Seat?

Coin Flip Game: Can You Win with Fewer Tosses?

atypicalquant
January 10, 2022January 4, 2024

Rick and Morty play a game where they flip 20 and 21 coins, respectively. What is the probability that Rick gets more heads?

Read More »Coin Flip Game: Can You Win with Fewer Tosses?

Logical Pirates’ Treasure Split: Who Gets What?

atypicalquant
August 1, 2021January 4, 2024

A crew consisting of 3 democratic pirates finds a bounty of 100 coins.

The strongest pirate must propose a bounty split and all pirates vote. If the vote passes, meaning that it gets at least half the votes, his proposal is accepted. If the vote doesn’t pass, he is killed, and the process is repeated.

Knowing that all pirates possess perfect logic and their priorities are, in order to survive, then more bounty, then more deaths, how will the coins end up being split?

Read More »Logical Pirates’ Treasure Split: Who Gets What?