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
For the coin toss, you’re right. Each coin toss is independent from the previous one. You have a 50% chance of getting tails each time. Imagine you tossed the coin 3 times but hid the results from him. Then he tossed it once. Does he have a lower chance of getting heads just because your previous tosses were all tails? Does him knowing whether they were heads or tails change how the coin flips in the air? Does the coin have a memory of all the times it’s been tossed in the past? If not, then by what mechanism is it going to know that it did heads the past 3 tosses and should do tails now? It doesn’t really make any sense to think that the previous events here could affect future events. Each time you throw the coin up there’s a 50/50 chance it will land on either side.
With the event that happens every 10 years it’s a bit trickier because that’s an expected value not a probability. Without more context, we don’t know how that expected value was calculated, so it could be imminent or it could be random depending on what it is. For example, imagine you’re filling a cup with water and it generally takes 5 seconds to fill it up. If it’s currently been 6 seconds, the chance that the cup will overflow is imminent, and is increasing over time, and so in that case you are on “borrowed time”. But if it’s something like a weather event or something random that isn’t directly tied to duration since the last event then you’re not on borrowed time for that. The 10 year value is just based on averages, not how long it takes to build up to the event. So it depends entirely on what it is and why the event is likely to occur “every 10 years”.
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