### Trick-or-Treaters Are Using the Executive Mindset

Haaaappy Halloweeeeen, dear reader. What’s that? You’re already annoyed by the trite conceit of this conveniently-timed piece about trick-or-treating? Read more

### AND vs OR Probability, The 1-x Trick, & Why the Orioles are 20/1 Odds to Win the World Series

*Note: This is the first of a two-part series on Probability. The baseball odds used in this article were true on the morning of October 11 and are definitely no longer true. Using this gambling advice will likely cost you money in the long run, as Joe will explain in Part 2.*

In terms of excitement, the World Series of Coin Flipping would rate right next to solving Data Sufficiency problems in the general public’s mind. But any Vegas oddsmaker worth his weight in comped beverages would be able to calculate the odds for every coin flipping contest in the time it would take the coin to land. In an 8-team bracket-style tournament, every squad would have 1 in 8 odds to win it all because only 1 team out of the 8 could outguess their way to the championship. But what if each matchup of two teams was a 3 game series? It wouldn’t affect the odds at the beginning of each series (still a 50% probability for each team to win), but once the first outcome was decided, those Vegas oddsmakers would require some knowledge of And Probability to keep the odds fair.

Imagine we have two teams competing in the first round of our Coin Flipping Playoffs- let’s call them Baltimore & New York. In our three game series, New York happened to have some late flipping heroics to go up 1-0. What are the odds that Baltimore comes back in this series and what are the odds that Baltimore comes back and then wins the whole tournament? The key to this type of question is understanding that many things have to go right in order for Baltimore to win it all- first they need to win Game 2, then win the winner-takes-all Game 3, then win their semi-final series, and then still have enough thumb strength to flip the World Series in their favor. Four unique events need to happen, and every single one of those events must happen for Baltimore to emerge victorious. Since the odds of each game and each series going Baltimore’s way would be 1/2, we can solve this by finding the odds that Baltimore wins Game 2 (1/2) AND Game 3 (1/2) AND the next series (1/2) AND the championship (1/2). In probability, whenever we want X AND Y to occur, we need to multiply the respective odds together. The odds of Baltimore winning Game 2 and 3 would be 1/2 x 1/2 = 1/4. The odds of winning all four events would be (1/2)^{4} = 1/16.

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