Another probability question

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Old Jun 6, 2011, 11:06am   #1
 
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Another probability question

Say you have a coin weighted to show heads 60% of the time. How many coin tosses are needed to have 90% confidence of getting more heads than tails?
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Old Jun 6, 2011, 11:08am   #2
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Re: Another probability question

toss the coin until you have more heads than tails.

then you can be 100% confident that you have more heads than tails.
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Old Jun 6, 2011, 11:24am   #3
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Re: Another probability question

The market is very slow today and coin tossing seems to be all the rage. I am curious, though. Why go to all that trouble only to make the coin weighted for 60% heads ? If you are going to tamper with it, isn't it better to make both sides of the coin heads ? Then you are 100% certain of a win, 100% of the time.

Also is there something special about 60% that people keep mentioning it. I am puzzled as I prefer 100%.
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Old Jun 6, 2011, 1:20pm   #4
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Re: Another probability question

I prefer a coin with 30% heads that pays 10 heads and losses 1 for tails.

Expected win: 0.3 x 10 - 0.7 x 1 = 2.3

What about that?

I agree, nothing special with 60%. It is just a bug in their head. They need some reprogramming.
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Old Jun 6, 2011, 1:35pm   #5
 
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Re: Another probability question

WinstonSmith started this thread That's all well and good Albert - top marks for understanding expectancy. But can you solve the probability question?
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Old Jun 6, 2011, 1:44pm   #6
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Re: Another probability question

2.512941595
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Old Jun 6, 2011, 1:49pm   #7
 
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Re: Another probability question

WinstonSmith started this thread I feel some uncertainty Mr Bramble...
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Old Jun 6, 2011, 1:53pm   #8
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Re: Another probability question

That's definitely a good thing.
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Old Jun 6, 2011, 1:53pm   #9
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Re: Another probability question

41
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Old Jun 6, 2011, 3:06pm   #10
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Re: Another probability question

What am I thinking!!! Read the question Brambs...

You want 90% probability of MORE heads than tails. Sorry.

4.507575552
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Old Jun 6, 2011, 5:17pm   #11
 
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Re: Another probability question

Quote:
Originally Posted by WinstonSmith View Post
Say you have a coin weighted to show heads 60% of the time. How many coin tosses are needed to have 90% confidence of getting more heads than tails?
in this experiment tossing the coin will prove nothing
because the nature of the coin has allowed us to pre work out the proberbility
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Old Jun 6, 2011, 5:37pm   #12
 
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Re: Another probability question

WinstonSmith started this thread
Quote:
Originally Posted by 6am View Post
41
Spot on 6am, as given by this calculator:

http://stattrek.com/Tables/Binomial.aspx
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Old Jun 6, 2011, 5:40pm   #13
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Re: Another probability question

Oi! Do you have any idea how long it took me to create a weighted coin..

4.507575552
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Old Jun 6, 2011, 5:46pm   #14
 
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Re: Another probability question

WinstonSmith started this thread My sympathies Mr Bramble, but how did you know when you'd thrown 4.507575552 tosses?
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Old Jun 6, 2011, 6:05pm   #15
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Re: Another probability question

If I’m honest, after setting up the smelter and the die casting tools and getting the damned thing weighted at precisely 60% heads and 40% tails (couple of hundred prototypes), I was knackered. So I just guessed at the result. I imagine it was the degree of precision that gave it away really.

It may not be totally accurate at 4.507575552, but you have to admit it looks a lot more precise than 41.

On a serious note, and I don’t dispute the beauty, complexity and deeply rigorous nature of the mathematical formula involved, I can’t help feeling that even with a fairly weighted coin, you’d have a 90% probability of getting more heads than tails a lot sooner than 41. Perhaps my grasp of probability is so far out of whack with reality (wouldn’t be the only thing that is) that I am pleasantly surprised by such things, or, it could be, reality doesn’t conform to the statistical straightjacket within which we pretend to place it to so easily convince ourselves our models adequately mirror reality.

Something to test out with a real coin while waiting for the plane that never takes off to take off.






Anyone want some dodgy coins.....
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