Another probability question

[WinstonSmith]

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?

 

[DashRiprock]

toss the coin until you have more heads than tails.

then you can be 100% confident that you have more heads than tails.

 

[BeginnerJoe]

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%.

 

[Albert Carey]

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.

 

[WinstonSmith]

That's all well and good Albert - top marks for understanding expectancy. But can you solve the probability question?

 

[TheBramble]

2.512941595

 

[WinstonSmith]

I feel some uncertainty Mr Bramble...

 

[TheBramble]

That's definitely a good thing.

 

[6am]

41

 

[TheBramble]

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

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

4.507575552

 

[Emini-mouse]

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

 

[WinstonSmith]

41

Spot on 6am, as given by this calculator:

http://stattrek.com/Tables/Binomial.aspx

 

[TheBramble]

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

4.507575552

 

[WinstonSmith]

My sympathies Mr Bramble, but how did you know when you'd thrown 4.507575552 tosses?

 

[TheBramble]

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.....

 

[amit1986]

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.

Depends on the weight of the coin. 60% isn't much far from 50% standard coin, so it makes sense you'd have to toss it many times to reach that confidence level.

Perhaps my grasp of probability is so far out of whack with reality (wouldn’t be the only thing that is)

Definitely true in your case !

 

[coopster]

I would never have 90% confidence. The only way you can be any more "confident" is to record what was thrown before.

If i threw a tails, the chance was 0.4 = 40%
I Threw again, the chance of another tails is 0.4 x 0.4 = 16% Threfore chance of heads = 84%
I Threw again, the chance of yet another tails is 0.4 x 0.4 x 0.4 = 6.4% therefore Heads = 95.4%

You could say "statistically" the chances of a heads are improving but they are still really only 60% each time as each toss is independant of the previous tosses :smart:

I think thats right. Would've been easier to look at google instead of giving me the opportunity to waste my time! :idea:

 

[Hotch]

Faith in humanity...waning....

 

[Emini-mouse]

your all barking up wrong trees on this thread
or im just barking

 

[TheBramble]

It's Ok, they're binary trees.