I recently had a disagreement with a friend about what it means for an event to have a probability of happening every X times.
Take for example a coin that if flipped has a 50% probability of landing heads and a 50% probability of landing tails.
My understanding is that while the probability of landing tails 3 consecutive times is smaller than that of landing it 2 consecutive times, if in the last two flips you got tails it has no effect on the probability of you getting tails in the following coin flip.it stays 50-50.
But he seems to believe that the probability of you getting tails gets smaller and smaller the more you land multiple consecutive tails.which sounds very counter intuitive to me.
For a more concrete example, he seems to think that if an event has a probability of occuring every 10 years, and it’s been more than 10 years since the last time it occured, we are living on borrowed time and the probability of it happening now is extremely high while I think it had the same probability of occuring today than it had of occuring 9 years ago.
Which one of us is wrong, please give examples.
In: 5
Your concrete example is actually less concrete than the coin. It depends on what the process that generates the event it. e.g. If a volcano usually erupts every 10 years, and it’s been 12, then that eruption is much more likely to happen. In that cases, it’s because the event (eruption) is the culmination of a process (geological stuff that I know basically nothing about), and if the event hasn’t happened, the underlying cause it still accumulating.
Your coin flip on the other hand has no such process. You simply decide to flip and then do. That makes the coin flip you’re doing right now completely independent from the prior flips, so your next flip is 50/50 no matter what the prior ones looked like.
On a fun side note here, if your friend really wants to cling to this, offer to play a game with them. You’ll start flipping a coin; at any time they can stop you and say that they are willing to bet on the next flip. If they’re right you pay them $3; if they’re wrong they pay you $4. If your friend’s model was correct then they could easily make money from you by just waiting for 2 in a row and then betting the opposite. However, your friend’s model is incorrect and you’ll take them to the cleaners. I worked a similar plan against a buddy in college while demonstrating the Monty Hall Paradox; I bought a cheap 6 pack and gave him the rest back after. 😛
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