Hello everyone! Have you ever read in the newspaper on the Internet about some amazing coincidence or unlikely event?
and it will say something like "it was a one in a million chance", but still, it happened.
Well, the point is that even unlikely events will happen if you give them enough opportunities
For example, flipping 10 heads in a row. Well that's about one in a thousand
when in fact it's a half to the power of 10, which is 1 in 1024.
Now, if you perform the experiment 1024 times you might expect it to happen once
In fact you may have seen the magician Derren Brown try this and it took him 9 hours
Now, was he lucky or unlucky? Let's find out, I'm gonna do it!
Here's my coin, I will show you. There's the Queen there. there's the Queen's face
On the other side there's the tail which I've marked with a big X, cross, no, this is bad, this is the failed tail right there.
Now, let's try it out, this is my first attempt, I'm gonna flip the coin into the bowl
*DLING*
And I get... A tail! Not a good start, but still, that's one down, 1023 to go.
And that's exactly what I did: try after try, coin after coin, continuously flipping the coin,
until I got 10 heads in a row.
I knew most of my attempts would not be succesful. In fact the vast majority, nearly 90%, would end on only the first, second or third trial
On the plus side that meant I could stop the trial as soon as I saw a tail, which meant I could save a lot of time.
Even so, like ?, I was fully prepared that 1024 attempts would take 9 or 10 hours
Yet it's even worse than that. If I tried the experiment 1024 times, I expect 1 success, but that's an average!
I might three successes, I might get two, I might fail completely, I might try 1024 times and fail every single time.
In fact I knew that. If the probability of success was 1 in 1024, than the probability of failure is 1023 in 1024
And the probability of failing every time would be that to the power 1024. That's the number of trials I intended to perform.
That means the probability of total failure was about 37%.
Success then was 63% but in no way guaranteed. But I kept trying and trying until one hour in and on trial 234...
Head.
Two heads.
Three heads.
Four heads.
Five heads.
Six heads.
Seven heads.
Eight heads.
Nine heads.
Ten heads.
Ten heads in a row!
Success and not sooner than I expected. So I could have stopped right there I decided to complete the experiment to finish the 1024 trials.
But since I had already had 1 success that means I wouldn't get another now.
Well I knew that wasn't true because a coin has no memory and success in the past would have no effect on success in the future.
Even so I only had 790 trials to go so I knew the probability of total failure from this point on would be about 46%
Meaning I still had a better than half chance of another success.
Yet, unfortunately for me, in the next five hours, no further look, but it does go to so that even unlikely events happen if given enough opportunites.
Even if you can't predict exactly where and when they happen.