Why probabilities are decieving

A friend on facebook recently posted something that stuck in my mind as a interesting topic to discuss here…

Take out a standard deck of 52 cards. Pull out 5 cards at random. The odds of having drawn your current hand are 1 in 311,875,200. That’s one in 311+ million for every 5 card hand you’ve ever been dealt in your entire life. Think about that next time someone tells you “X couldn’t have happened this way because it’s a one in a billion chance”! – Leart Shaka

This topic has come up many times in conversations, and in many different ways.

If you think about how many “events” there are in your day (hitting the red light instead of the green, song comes on the radio, the daily lunch special at the local deli, etc) you’ll get some gigantic number of points that “something” happens. I can’t recall where off hand, but at least one podcast a while back, talking on a related subject, mentioned that there are an estimated 10,000 – 20,000 “events” per day per person who lives a “typical” lifestyle (goes to work/school, sees other people on the street/hallway, etc).

Now for the sake of being bit more conservative, I’m going say 1,000 “events” per day per person for my example here.
In the United States there are over 300 million people.
Worldwide there are over 6 billion.
The average life expectancy today is estimated to be 65 years (or 23,725 days).

Now if each of those people has on average 1,000 “events” per day in their life we can look at this a few different ways:

• Every person alive at the moment combined will experience 142,350,000,000,000,000 total events. (This one is actually pretty meaningless, but I just thought it was a cool number to include; but I promise the next two actually mean something)
• On average, people will experience 23,725,000 “events” in their life.
  If an event is “one in a million”, you should actually expect that to happen 23-24 times in your life.
• Sticking with the idea of “one in a million”, there are 6 trillion “events” happening each day to people, meaning there should be on average 6,000,000 “one in a million” events worldwide per day.
• And keep in mind, these estimates are 1/10th or less of the actual estimates of number of events per day per person.

So the next time somebody says “what are the odds of that happening?”, you should reply “pretty fucking good actually”…