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
The probably of an event depends on what the event is. If you are asking what is the probably that you get 3 tails in a row its 0.5³ so 0.125, 12.5%. But the coin flips themselves are independent so if you had two tails the probably that the third one will be tails too is 50%. Getting those two tails in a row already had a probably of 25% but that happened. Probably is about asking what can happen in the future and independent coin flips dont effect each other.
Its always good to write out the possibilities:
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
If you got TT for the first two you will either get the TTH or the TTT scenario. 50% probability for each.
From the start the TTT scenario is 1/8 of all the possibilities, getting either of those scenarios are equally likely but when you already got two tails 6/8 of those scenarios are no longer possible so that leavs 50-50 odds.
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