Even a rudimentary look at probability can give new insights about how to interpret data.
Simple thought experiments an can give new insight into the different ways misunderstanding of statistics can distort the way we perceive the world.
We've selected five classic problems solved in unconventional ways that can help one get a new way to understand the way that data can be misleading and the story on the surface can take people in the wrong direction.
The Monty Hall Problem
Say you're on a game show where there are three doors. Behind two of the doors, there are goats. Behind one of the doors, there is a brand new car.
The host says that once you pick a door, he'll open one of the doors you didn't pick to reveal a goat. Then, you have the option of either staying with your door or switching to the last unopened door.
Do you switch or stay?
Answer: Switch
This is actually based on a real game show, and the result has been the source of controversy for years.
Essentially, when you first made the selection, you had a one in three chance of correctly selecting the door that had a car behind it. Switching raised that probability to two in three that you'll select a car.
Said another way: A player whose strategy is to always switch will only lose when the door they initially selected has a car behind it. A contestant who selects either of the two doors with a goat behind it and then switches will always get the car.
Here's a final way to look at it, provided the contestant selected Door #1
Door 1 Door 2 Door 3 Result if Stay #1 Result if Switch
Car Goat Goat Car Goat
Goat Car Goat Goat Car
Goat Goat Car Goat Car
Source: The Straight Dope
The Birthday Paradox
You run an office that employs 23 people. What is the probability that two of your employees have the same birthday? For the purposes of the problem, ignore February 29.
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