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
You are generally right. It depends on the circumstances of the circumstances of the problem.
If one event has an impact on the next even the next event, then his reasoning is good. An example of this would be drawing red balls out of a bag instead of yellow. There is a finite number of red balls in the bag, ao every time you draw another one out, the odds get higher against it happening again.
However if prior events have no impact on the next event, like your example of a coin flip, then the odds don’t change, so it would stay 50/50 as in your example.
If he still doesn’t understand it, ask him to explain to you how the previous coin flip physically impacts this coin flip. He won’t be able to do it.
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