Heads I Win: Probability and Mechanics of Coin Flipping

[PhanthomJay]

Question 1.

If I flip an unbiased coin a hundred times, I should get about 50 heads and 50 tails. Once in awhile it will be exacly 50 of each, but usually it will be a 49/51 or 47/53 split or something like that. What is the probabiliy that it will be exactly a 50/50 split?

Question2.

Can I build a flip coin machine that will flip an unbiased coin in such a way (certain applied force,angle, twist of the flip in still air, always the same initial starting conditions and no bounce to the coin when it lands) such that it will come out heads all the time, or close to all of the time, or exactly every time.

Thanks.

 

[D H]

This looks like homework, Jay. You know the rules on homework by now. Where's your work? For question 1, what are the relevant equations? For question 2, what do you think?

 

[PhanthomJay]

This looks like homework, Jay. You know the rules on homework by now. Where's your work? For question 1, what are the relevant equations? For question 2, what do you think?

Come on, D H, I'm getting too soon oldt to be doing homework. If this was a homework question, I'd have posted it there, and you know that. Actually, I'm trying to compare everyday life probabilities with quantum probabilities (I'm reading Hawking's new book). Can you help? If not, forever hold your peace

My thoughts? Question 1: 50-50; Question 2, since the event is no longer random, the question has no answer. And here's a 3rd question, what is the probabilty of a 47/53 split under the first scenario? I'm guesing 50-50 again.

I was going to suggest you report this post to a mentor, but since you're one of them, that won't do much good

P.S. I struggled to get a C in Statistics 45 years ago.

 

[skeptic2]

Can I build a flip coin machine that will flip an unbiased coin in such a way (certain applied force,angle, twist of the flip in still air, always the same initial starting conditions and no bounce to the coin when it lands) such that it will come out heads all the time, or close to all of the time, or exactly every time.

Probably not very hard to do.

When I was a kid I practiced flipping a coin so it would always come up heads (or tails) and was able to do it slightly over 70% percent of the time. Since then I've been very wary of using a coin flip as a random indicator.

 

[ctrl_shift_T]

My thoughts? Question 1: 50-50;

I don't think the answer is 1/2.
There are ¹⁰⁰C₅₀ possible ways of getting 50 heads in 100 tosses.
And probability of any 1 of these is (0.5)^100

I think the probability has to be ((0.5)^100 )*(¹⁰⁰C₅₀).

The calculation is available on wolfram alpha :-
http://www.wolframalpha.com/input/?i=(100+choose+50)*2^(-100)
http://www.wolframalpha.com/input/?i=100+coin+tosses"

And here's a 3rd question, what is the probabilty of a 47/53 split under the first scenario?

The answer to this should be ((0.5)^100)*(¹⁰⁰C₄₇)
http://www.wolframalpha.com/input/?i=(100+choose+53)*2^(-100)

 

[PhanthomJay]

Thanks, all. Now I'm not sure why I asked the question. I think my grade was more like a D . Back to the book...

 

[DaveC426913]

Question2.

Can I build a flip coin machine that will flip an unbiased coin in such a way (certain applied force,angle, twist of the flip in still air, always the same initial starting conditions and no bounce to the coin when it lands) such that it will come out heads all the time, or close to all of the time, or exactly every time.

Thanks.

Well ... yes. This is trivial.

Have the machine drop the coin without any flipping at all. It will land on the same side 100% of the time.

I know that's not what you were thinking; I'm forcing you to ask yourself what it is exactly that you wanted to build.

If you want to have it land the same way up, why bother with the flip at all? Unless it is to fool someone into thinking it was a fair toss...

 

[PhanthomJay]

Well ... yes. This is trivial.

Have the machine drop the coin without any flipping at all. It will land on the same side 100% of the time.

I know that's not what you were thinking; I'm forcing you to ask yourself what it is exactly that you wanted to build.

If you want to have it land the same way up, why bother with the flip at all? Unless it is to fool someone into thinking it was a fair toss...

I don't want to build anything... I guess what I'm asking is this: If the answer is 100 percent, is this a violation of the Heisenberg Uncertainty Principle?

Or better yet, can you respond to my post in the Quantum Physics forum:

https://www.physicsforums.com/showthread.php?t=459568

Thanks!

 

[DaveC426913]

I don't want to build anything... I guess what I'm asking is this: If the answer is 100 percent, is this a violation of the Heisenberg Uncertainty Principle?

Well, we're talking about a macroscopic object here. The chances of the coin not landing on the same side are similar to the chances of the coin tunnelling through the table and appearing on the other side, or of all the air in the room suddenly moving to the left half of the room. See?

 

[PhanthomJay]

Well, we're talking about a macroscopic object here. The chances of the coin not landing on the same side are similar to the chances of the coin tunnelling through the table and appearing on the other side, or of all the air in the room suddenly moving to the left half of the room. See?

Yes, I see, thanks.

Now if I can just see that March moon...

 

[awkward]

Question 1.

If I flip an unbiased coin a hundred times, I should get about 50 heads and 50 tails. Once in awhile it will be exacly 50 of each, but usually it will be a 49/51 or 47/53 split or something like that. What is the probabiliy that it will be exactly a 50/50 split?

[snip]

You already have found the exact answer via the Binomial distribution, but you can get an excellent approximation with less computation using the Normal approximation to the Binomial. The total number of heads has a mean of 50 and a standard deviation of 5. If you evaluate the pdf of a Normal distribution with that mean and standard deviation at x = 50, I think you will find the result is very close to the probability given by the Binomial.

 

[honestrosewater]

Can I build a flip coin machine that will flip an unbiased coin in such a way (certain applied force,angle, twist of the flip in still air, always the same initial starting conditions and no bounce to the coin when it lands) such that it will come out heads all the time, or close to all of the time, or exactly every time.

Since your question seems philosophical in spirit, I'll share my slightly different interpretation of this question. If the coin always comes up heads, I'd say "the coin" is not unbiased (since I normally define the bias of coin based solely on the outcome). If you want to distinguish between the coin and the flipping process, if the flipping process is biased/rigged, it doesn't matter what the coin is, or there is no way of inferring its bias. No? You can build a machine to flip a biased coin predictably just as easily (theoretically) as you can build one to flip an unbiased coin predictably. No? You'd have to inspect the machine to find out.

 

[DaveC426913]

Now if I can just see that March moon...

[ font=haunting ]There is no March Moon for you here. Only heartbreak and tears.[ /font ]

 

[bpet]

The answer to this should be ((0.5)^100)*(¹⁰⁰C₄₇)
http://www.wolframalpha.com/input/?i=(100+choose+53)*2^(-100)

With Stirling's approximation P[N=50+x] ~ exp(-99*x^2/5000)/sqrt(2*pi)