Question about probability - Page 1

[ARCHIVED THREAD] - Question about probability

Posted: 6/19/2018 7:43:00 PM EDT

Flip a coin 5 times. The probability of hitting all heads is of course 1 in 2^5, or 1/32.

Now say you actually run this test exactly 32 times.

What is the probability that at 5 heads appears once?

Bonus points for general solutions.

Posted: 6/19/2018 7:55:09 PM EDT

[#1]

That's not completely accurate, no two faced coin weighs the same on both sides nor will wind drag act repetitively on coins with differing faces and the flip will not be consistent without major planning.

Lots of variables

But I do know the answer that is closest to what you would expect the answer to be

Posted: 6/19/2018 8:06:17 PM EDT

[#2]

Do you know how to answer the question or not?

Posted: 6/19/2018 8:08:25 PM EDT

[#3]

Did I really need to preface this question by saying this is a mathematically fair coin, being flipped mathematically randomly? Would that make you happy?

Posted: 6/19/2018 8:10:04 PM EDT

[#4]

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Quoted:
Do you know how to answer the question or not?

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Yes I do.

You may want to reword your question first.

Posted: 6/19/2018 8:16:00 PM EDT

[#5]

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Quoted:
Did I really need to preface this question by saying this is a mathematically fair coin, being flipped mathematically randomly? Would that make you happy?

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There are still far too many variables to give an accurate answer from your OP.

Can a flip be from tails up to heads up only completing 1/2 revolution or does a flip mean only 1 full flip in which case it would always land on what it started from?

What about a consistent 1.5 revolution flip, that's repeatable.

There are many more variables at play to contend with according to the OP, but I'm sure I know what you are trying to ask and I'm sure I know the answer.

Chance favors the prepared.

Posted: 6/19/2018 8:16:56 PM EDT

[#6]

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Quoted:

Yes I do.

You may want to reword your question first.

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Have a nice day. I’m not going to play 20 questions trying to out-pedantic you.

Any non pompous asses are still welcome in this thread.

Posted: 6/19/2018 8:23:57 PM EDT

[#7]

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Quoted:

Have a nice day. I’m not going to play 20 questions trying to out-pedantic you.

Any non pompous asses are still welcome in this thread.

View Quote

I guess your OP is flawed from the get go. I can flip a coin just once, I can flip it up in the air all willy nilly.

You need some parameters in order to get results to this question

What the fuck does "What is the probability that at 5 heads appears once?" Mean?

Posted: 6/19/2018 8:24:10 PM EDT

[#8]

OP, assuming you have a fair coin and a fair flip, the following is the solution (unless I'm totally an idiot, which is possible):

You have to look at the probability of 5 heads happening in a single set of five. As you've stated, in 5 flips the probability of getting 5 heads is 1/32. This means the probability of not getting 5 heads is 31/32.

So what is the probability of having this happen 32 times in a row? Well, it is 31/32^32 or roughly 36.2%.

This means, if you did 32 5 flip trials, you'd have a 63.8% chance of getting at least one that is all heads.

Posted: 6/19/2018 8:44:21 PM EDT

[#9]

Quote History

Quoted:
OP, assuming you have a fair coin and a fair flip, the following is the solution (unless I'm totally an idiot, which is possible):

You have to look at the probability of 5 heads happening in a single set of five. As you've stated, in 5 flips the probability of getting 5 heads is 1/32. This means the probability of not getting 5 heads is 31/32.

So what is the probability of having this happen 32 times in a row? Well, it is 31/32^32 or roughly 36.2%.

This means, if you did 32 5 flip trials, you'd have a 63.8% chance of getting at least one that is all heads.

View Quote

Thank you.

That makes complete sense that way.

Posted: 6/19/2018 10:11:17 PM EDT

[#10]

Quote History

Quoted:
OP, assuming you have a fair coin and a fair flip, the following is the solution (unless I'm totally an idiot, which is possible):

You have to look at the probability of 5 heads happening in a single set of five. As you've stated, in 5 flips the probability of getting 5 heads is 1/32. This means the probability of not getting 5 heads is 31/32.

So what is the probability of having this happen 32 times in a row? Well, it is 31/32^32 or roughly 36.2%.

This means, if you did 32 5 flip trials, you'd have a 63.8% chance of getting at least one that is all heads.

View Quote

Cool. Thanks.

Posted: 6/19/2018 10:22:43 PM EDT

[#11]

Still 1 in 32. Your damn coin doesn't have a memory.

Posted: 6/20/2018 10:22:01 AM EDT

[#12]

The chance of getting exactly one result of 5 heads in 32 trials:

Steps
1/32 = the chance of getting 5 heads when flipping a coin 5 times (1/2)^5

31/32 = the chance of not getting 5 heads from flipping the coin 5 times (1 - 1/32, from the previous line)

1/32 * (31/32)^31 = chance of getting 5 heads in the first trial, and not getting 5 heads in each of the remaining 31 trials

= (31^31)/(32^32)

= .01168, or about 1 in 90

The chance of getting that 1 result in any specific trial is the same as getting it in the first trial, so the total chance is simply adding up the number of possible slots for it to occur in (32), so we take that number and multiply it by 32 and get our final probability, which becomes .37373, or just over 37%.

Mike