# Getting to the party in time | The Flaw of Averages

Project Summary
Calculating all possible outcomes for people to arrive at a party at the same time (according to the Flaw of Averages by Sam L. Savage)
Created
January 16, 2022
January 16, 2022

With a nod to Sam L. Savage I've spent the last weeks wrapping my head around probability simulations and other interesting topics. In "The Flaw of Averages" Savage explains why using an average number can lead to small or big mistakes in all areas of life.

The party problem is a very simple one.

You want to go to a party at 6 p.m. –– you and 1 friend want to carpool from your house at 5.30 p.m. –– The party is 30 min away from your house.

There are 2 people that want to carpool together. There is a 50% chance that each one of you makes it in time to your house. The calculation for the average would be (50% + 50%) divided by 2. On average, your chance of making it in time is 50% –– but that's WRONG!

Imagine, if each person's chance of arrival would be represented by a coin flip 🪙

The outcomes could be as follows:

• A makes it in time, B misses the train.
• B makes it in time, B is stuck in traffic.
• A and B are both late.
• A and B make it in time and arrive together at the party.

The probability of them making it is 25,00% or 1 in 4

This very simple example lead to a little excursion of mine into the realm of Google Sheets where I searched for a way of visualising all possible coin flips for 2-10 people. Well, it took me some Googling and Experimenting but I found some elegant way to calculate 4-1024 outcomes directly inside a Google Sheet. Hit the button to try it out!

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