Coin Toss odds

[Lotus Lewis]

Hello everyone
Last night in the pub a question came up and it was

what's the odds if i toss a coin ten times and it landing on heads every time ?

1 in ? what chance

Edited by Lotus Lewis on Saturday 3rd October 08:22

[Jem Thompson]

I think it is 0.5^10. Ready to be proved wrong however.

[Overhaulin]

Jem Thompson said:

I think it is 0.5^10. Ready to be proved wrong however.

Yep,so odds of 1 in 1024

.5*.5*.5*.5 etc =0.000977

1/0.000977 = 1024

[Craigyp79]

Is that factoring in the chances of it landing on the side?

[Blib]

It came up heads 90 times in a row for Rosencrantz.

Poor sod.

[AJS-]

Assuming the coin isn't biased to one side then every toss is independent of the last. Each throw has a .5 probability of landing heads and a .5 probability of landing on tails, 10 or 100 times in a row.

[whitevanman88]

Presumably the way it is tossed / starting side would also have - an albeit small - effect?

[moosepig]

AJS- said:

Assuming the coin isn't biased to one side then every toss is independent of the last. Each throw has a .5 probability of landing heads and a .5 probability of landing on tails

Correct.

AJS- said:

(whether) 10 or 100 times in a row.

It is true to say that all throws are independent, but if you take the problem of 10-in-a-row as atomic then there are 2^10 possible outcomes. Consider a 10-digit binary number where 0 and 1 represent heads and tails. There are 1024 of these from 0000000000 to 1111111111. Only 1111111111 represents the desired outcome, the other 1023 do not match. All combinations have equal probability of occurring, hence 1 in 1024.

Edited to sort out quoting

Edited by moosepig on Saturday 3rd October 13:58

[Schmeeky]

at the above... although there is the chance the coin could land on its edge....but that would be vanishingly small on a hard surface - flipping the coin over a deep shag-pile carpet would have a greater chance of landing on its side.

[Tony*T3]

Lotus Lewis said:

Hello everyone
Last night in the pub a question came up and it was

what's the odds if i toss a coin ten times and it landing on heads every time ?

1 in ? what chance

Edited by Lotus Lewis on Saturday 3rd October 08:22

It depends on the context. If you say you are going to toss a coin 10 times and you predict its going to land heads up ten times in a row, then the odds are as stated above - 1024 to one, or whatever.

However, if your just tossing a coin and you happen to notice it just happens to land heads up 10 times in a row, then the odds are still 50/50 every time you toss the coin. Thats because the coin is an inanimate object, and has no memory or concept of 'odds'. its still only got 2 viable outcomes (we can discount the landing on its edge outcome).

Only you as a human, with a brain, can see a 'pattern' or 'history' of the coin toss. Once you toss the coin and pick it up again, all reference to the previous events is gone, apart from in your mind. (assuming your on your own and its not being filmed or whatever).

The coin itself has no memory and no history. If you werent observing it, there would be no multiplication of the odds. A dog could be watching you and he's not going to think 'dude, ten times in a row, the odds are massive', is he? Because he has no concpet of maths.

So if you happen to toss a coin in the air ten times and it lands heads up 10 times in a row, you, with a reasoning brain, will say to yourself 'wow, the odds on that are 1024 to one, who would believe it?' Would the odds now of throwing an eleventh head in a row be 1024 x 2? No, still 50/50. All previous results are merely recorded and analysed by your brain and turned into maths.

Predicting an event in advance is where odds and mathematics come into play. An event actually just randomly happening 10 times in a row will only be pertinant if witnessed by someone with the mental capacity to work out the odds. This is were most people fall foul of the lottery, beliveing that their odds might improve the longer they play the same numbers. The odds never change, week to week, and the balls have no 'history or memory'.

Same with the roulette wheel (if its totally fair and not been intereferred with). People often see patterns and runs with previous outcomes and will bet accordingly. However, any continuation of a pattern or run, or break in pattern or run, is merely random and only observable by a human. 'Its been red 10 times in a rod, it must be black next', as the odds on it being red 11 times in a row are massive. Um, no, the odds are still exaclty the same. Whats happened in the past is irrelevant to the future outcome.

So its down to context. Only we see patterns and calculate odds. No matter how many times you throw the coin in the air, there are only two reasonable outcomes. Heads, or tails. There are tens of thousand of different species on the planet, only we concrn ourselves with whats happened in the past and what could happen in the future.

[moosepig]

Tony*T3 said:

Lots of good stuff

+1

A good illustration is the difference between the following two examples:

1. What's the probability of throwing 10 heads in a row? (answer: 1 in 1024)

2. I have just thrown 9 heads in a row, what's the probability of throwing a tenth? (answer: 1 in 2)

[GTIR]

U lot is well clever.

You lost me at "Hello"

[Richjam]

Maybe they should get out more.......................

[GKP]

what's the collective noun for coin tossers?

[V8mate]

GKP said:

what's the collective noun for coin tossers?

[g4ry13]

It's 50/50 - it either happens or it doesn't.

[jamiebae]

Wasn't there a recorded incident of a coin landing on its side in a scientific experiment somewhere a couple of years back?

[GTIR]

jamiebae said:

Wasn't there a recorded incident of a coin landing on its side in a scientific experiment somewhere a couple of years back?

Possibly, but I would have fallen asleep way before then.