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
>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.
Your understanding is correct here. The thing we have to keep separate is the *probability of one thing happening,* and the *probability of multiple things happening.* Let’s pretend I’ve just flipped 3 heads in a row. What are the odds of my text flip being heads? 50%, because that’s just the odds of *one thing happening*. But what are the odds that I flip a coin 4 times and get all 4 heads? Well that’s only 1 in 16, or 6.25%, because that’s the odds of *each* of those coin flips put together. So you have to distinguish if you’re looking at just one event, or the sum of all of the events. The odds of a roulette wheel landing on 15 are 1 in 38, and the odds of landing on 15 twice in a row are around one in 1400. But if it’s already happened once, you can ignore that part of the odds, they’ve already happened – the odds of the next spin is still just 1 in 38.
Another way to think about it is to imagine a poker hand – imagine that you have a royal flush 10-J-Q-K-A all of one suit (let’s say clubs, for the example), that’s the rarest possible hand, right? Well now imagine that you have a 2 of spades, a 6 of diamonds, an A of hearts, a Q of diamonds, and a 10 of clubs. Well that’s a really common hand, right? Actually, it’s *exactly as rare* as the royal flush – both hands have the same seriously tiny chance of being dealt to you. We just see the good hand as significant and the trash hand as insignificant, so we don’t think of it that way. But it’s the same with many random events – the odds of getting three spins on a roulette wheel of 14-27-6 are *exactly* the same as spinning 32-32-32. We’d just call the first one “normal” and the second one “crazy,” because we see a pattern that we find interesting in one and not the other.
>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
This is a little different than the coin flip example, because a lot of real-world events aren’t totally independent, they’re dependent on a number of factors. Think of a volcano erupting for example – over time, magma will build up in a volcano, increasing pressure and increasing the odds of an eruption. There’s virtually a 0 chance of a volcano erupting a week after its last eruption, but a higher chance 5 year later, and a higher chance 10 years later (depending on the volcano, I guess), because the situation does change over time. Sometimes that can be the case for particular weather patterns or other events – they *may* become more likely over time. But it depends on the specific event, and what factors go into it – in some cases, the probability probably could get closer and closer to a near certainty over time.
Latest Answers