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 right about the coin. If you flip two heads, the third is still exactly 50-50. This is because every coin flip is independent of the others.
Your concrete example is more complicated and depends on your assumptions, and for practical purposes your friend is probably correct. If a geyser erupts every 10 minutes and 10 minutes has passed, it is much more likely the geyser will erupt in the 11th minute than it was in the 1st. This is because every minute that passes increases the likelihood of eruption. The eruption rate is *dependant* on time.
There really is no answer to your question without answering the question of if events are dependent or independent of one another
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