Maths question

[joe1]

I am told that when spinning a coin there is always a 50/50 chance of a head or tail .
So in 1000 spins there will be approx 500 of each.
If there has been 500 spins and all are heads is the probability of a tail next spin still 50/50.?

[mark01]

yes

[another-view]

Indeed, which is why money making schemes for casinos that tell you to wait for 6 reds to come up then bet on black are nonsense.

In the grand scheme of things 1000 spins is nothing. The figure approaches 50/50 as we near infinity spins.

[MarkRae]

Yes. As has been mentioned, these things are often more obvious than people would have you think, and what looks metaphysical to us is perfectly obvious logically.

Another classic is the probability that when dealing a round of whist all four players will have cards of only one suit i.e. North will have all hearts, East will have all spades etc. It's true that the probability of that happening is very low, but is exactly the same as the probability that any other given combination of cards will be dealt...

[another-view]

As is 1,2,3,4,5,6 being drawn from the lottery. People would think it has no chance but it has exactly the same outrageous odds as any other combination.

[MarkRae]

Correct. And, if it happened to be drawn tonight, the odds that it would be drawn again on Saturday night would be EXACTLY the same.

[jake-the-peg]

In theory this is all true.

In the real world if I saw 500 heads in a row I think I might start to suspect a dodgy coin don't you?

The odds of throwing 500 heads in a row are so small it makes a lottery win look an absolute cert

[vascop]

Or a dodgy person/machine spinning the coin.

[vascop]

And of course if somebody/something is fiddling, then the chances of another head coming up are very high indeed, certainly not 50/50.

[vascop]

And if they were fiddling things to get you to bet a thousand pounds on the next one also being a head, then they could probably fiddle a tail that time and you would then lose your money.

[wildwood]

Each spin as a separate exercise has indeed got a 50/50 chance but the odds of 500 heads coming up in a row are astonomical.

[Old_Geezer]

Don't choose 1,2,3,4,5,6 as your lottery numbers. There are loads of people who choose them thinking, no one else is going to be daft enough to choose 1,2,3,4,5,6 so if it comes up I'll take the lot.

[chakka35]

Old Geezer is right. The last I heard, the series 7,14,21,28 and 35 occurs about 20,000 times each draw and 1,2,3,4,5,6 about 10,000 times.

There is no meaningful set of numbers which has not been thought out by other people, which is why complete randomness is the only way to ensure the minimum number of other winners in the unlikley event of your winning.

By the way, casinos usually cash in when a series of say 5, 6, 7 blacks (or reds) comes up - because all the others are so sure that the other colour is BOUND to come up next after,say, three the same that they keep betting bigger and bigger sums on it.

[rov1200]

I have always questioned this type of probability. Like you say if the chance is 50/50 then overall you should get 250 of each. Therefore a run on the heads will mean more tails in future to achieve the 50/50 end result.

[another-view]

A popular misconception with such a small sample Rov. Try this out on the roulette table in Vegas and you'll soon come back home broke.

Let's say, I want to toss a coin twice and it comes down heads. By this 50/50 method, the next throw MUST be tails. 2 or 1000 is such a small number that it won't happen.

[Old_Geezer]

It is confusing, but as far as we can tell, fate doesn't hold a memory of what happened to the previous tosses, so the odds for any single toss remains the same. For a vast number of tosses you should expect to approach the 50:50 ratio, but you'd need an infinite number of tosses to see it for sure (and as we are dealing with infinities I'm not even that sure then :-) ).

[mollykins]

My brother was doing a piece of coursework on probability and had to flip a coin lots of times, one of the landed on its side and satyed there, what are the chances of that happening?