Coins Puzzle

[joules99]

If you flip a coin 19 times and it lands on tails all 19 times, what is the probability of it landing on tails the 20th time?

[THECORBYLOON]

biley you seem to be insisting on visual evidence of something before you believe it to be true. You are saying Kempie and I are wrong in our stating it is possible for a coin to land on its edge, you said it would be a miraculous event if it did. Miracles do happen and your faith tells you that. If a coin is tossed a million times it may land on heads exactly 500,000 times. It is also possible for it to land on heads 1,000,000 times. The odds of that happening are 1 in 2 ^ 1,000,000  so it's not likely BUT IT IS POSSIBLE.

Can you prove otherwise?

[gms]

There's a famous story in the Statistics department at Warwick University whereby the newly appointed Professor of Statistics, Jeff Harrison, was lecturing on probability. He attempted to demonstrate the 50:50 chance of a coin toss in front of the students and amazingly it landed on the table in front of him on its edge (without rolling off). I wasn't there, unfortunately, but as far as I know the story is true.

He hasn't managed the feat again yet, as far as I know......

[THECORBYLOON]

gms Thank-you for that. It is confirmed here and reading it, the odds were a billion to one.

[biley]

THECORBYLOON - Yes miracles do happen, I agree. But this is not a situation in which a miracle can occur - it either can happen or it cannot. (and if I did say that it would be a miracle if it did occur then I apologise). I am NOT stating you are wrong in the slightest (subsequent events might well prove you right) but I AM saying that you cannot say it CAN happen, with certainty, when you do not have proof that it CAN.

Yes, on this occasion the simplest way to prove it can happen is to have visual evidence of it. This question is simply not something that can be answered in any other way. It really is as simple as that. Where is the video recording that would prove it and that can be shown as final proof to all those (and if what I read is true, there are quite a few) who doubt, like me, that it can happen?

You may, as I say, believe it can happen, but you cannot be dogmatic about it until you have seen the proof - that is why I see no sense in kempie's original reply to gen2 and even less sense in his/her telling gen2 that he/she should have said something just because he/she (kempie) thinks that way.

In the same way that I cannot prove the Virgin Birth, and would certainly hope that I would never dogmatically insist on its being FACT, so, I believe, that  as you and kempie and others cannot prove a coin can land on its edge,(as yet at least), then those who believe that it can should also refrain from calling it a FACT.

[biley]

gms - thankyou for that. I think I may have heard that story before too. Sadly, it is doubtful whether there was a camera there to record the event so that we could all agree that yes, it can happen. Shame, because it is a great story. But that is all it is - a story. It is not proof because there could have been any number of things on that vinyl floor that stopped the coin from dropping on a head or a tail.

To all others - I may well go on looking for proof on this matter, as it intrigues me but for now let us agree that if gen2 had said originally that the odds of getting a tail the 20th time were exactly the same as they had been on the first and every subsequent toss, then this thread would not have been more than one post long!

[kempie]

biley - you seem to have got hung up on the phrase can happen implying that it means the same as will happen.

Of course it can happen; the only way it can't happen is if the coin doesn't have an edge to land on. That doesn't mean it will happen and I never said that it will happen only that it can (or may) happen. After all that is the whole point about probability.

[BPH]

Of course, if the coin landed in mud, it could easily end up resting in a vertical plane, ie neither heads nor tails. If it were tossed with a speed exceeding the escape velocity from planet Earth, it would disappear into outer space and not land at all. Am I being silly here? Yes, but no more so than some of the other contributors to this discussion. Get a life, guys! Devote your undoubted talents to solving some important problems, like world peace or global warming!

PS The answer is 0.5

[kempie]

BPH - you may jest but you have just reduced the probability even further to a figure lower than 0.5 by introducing the scenario that the coin may not land at all (e.g. someone snatching it out of the air).

[fordward]

Have you lot not got anything better to do

[kempie]

I'm just off to eradicate global warming and institute world peace ;-)

[BPH]

kempie, let me put my cards on the table. There are two approaches to this problem. EITHER we work with a theoretical "fair coin", which inhabits Maths textbooks, and which, BY DEFINITION, will land heads with probability 0.5 and tails with probability 0.5, independently of any previous tosses. OR we enter the world of physics, in which case we need to know a lot more to give an informed answer - like the position of the centre of mass of the coin, the initial linear velocity and angular velocity of the toss, the thickness of the coin, the nature of the surface upon which it lands (if it lands!) blah blah blah. Life is too short to debate the question using the second approach, so we must use the first, in which case the answer is 0.5 precisely. Thankyou and goodnight! 

[kempie]

But since none of us inhabits a maths textbook but rather a world governed by physics, why do so many people seem unhappy with an answer that is not exactly 0.5?

[THECORBYLOON]

biley there are thousands of hits mentioning the possibility of a coin landing on its edge. Can you quote ONE which says it isn't possible? Can YOU say why it's not possible? 

[BPH]

kempie: Beats me!

[gen2]

Wow!  I didn't realise my reply had started all this.  The question joules99 asked was a typical school statistics question and I just gave him the typical school statistics answer.  All you have succeeded in doing is to clog up joules99's mailbox.  So sorry joules99 if my original answer was not accurate enough, but you did not specify to how many decimal places you wanted the answer to be stated.

[THECORBYLOON]

That's right gen2 blame us for your inaccurate answer. I wouldn't worry but, it's prompted kempie to eradicate global warming and institute world peace.

[kempie]

... and such a noble endeavour is surely worth the nine emails generated by my posts.

[joules99]

ha i did not know for one minute this would be so controversial! anyway the question appeared on sky's braniacs and their answer was 50/50, the debate about the coin landing on it's edge is futile I think, because if it did it would surely roll and eventually fall over on one or other side, and not just stop dead? If you include this as an option you might aswell add the fact that their could be no outcome atall, for example if the world was destroyed by a meteorite while the coin was in mid air, if you accept that this is a possiblility, however small that this could happen then there is now 4 possibilities, not 3, or 2!!!!??