Basic Probability

This is a discussion on Basic Probability within the The Foyer forums, part of the Off the Grid category; If the probability of my flipping a head on any one toss of a fair coin is 1 in 2 ...

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Old Mar 27, 2009, 11:45am   #11
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TheBramble started this thread If the probability of my flipping a head on any one toss of a fair coin is 1 in 2 this implies that with any two tosses of the same coin, I should expect, statistically, to get (at least) one head.

(Same applies if I was looking to get a Tail, obviously.)

And if you are all correct, which Iím sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that Iíd need to flip a fair coin 4 times to be reasonably certain, statistically, of getting (at least) one occurrence of two heads.

(Same applies if I was looking to get two consecutive tails, obviously).

Is this correct so far?
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Old Mar 27, 2009, 11:55am   #12
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Originally Posted by TheBramble View Post
If the probability of my flipping a head on any one toss of a fair coin is 1 in 2 this implies that with any two tosses of the same coin, I should expect, statistically, to get (at least) one head.

(Same applies if I was looking to get a Tail, obviously.)

And if you are all correct, which Iím sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that Iíd need to flip a fair coin 4 times to be reasonably certain, statistically, of getting (at least) one occurrence of two heads.

(Same applies if I was looking to get two consecutive tails, obviously).

Is this correct so far?
Yes.
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Old Mar 27, 2009, 12:06pm   #13
 
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yes. as per THM.
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Old Mar 27, 2009, 12:08pm   #14
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TheBramble started this thread I think Iím with you all so far. Just.

If I flip a fair coin 4 times, youíre saying I could expect two consecutive tails with a probability of 1 in 4 and of two consecutive heads with a probability of 1 in 4, but I can expect two consecutive tails or two consecutive heads with a probability of 1 in 2.

Have I understood you all correctly?
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Old Mar 27, 2009, 12:14pm   #15
 
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Originally Posted by TheBramble View Post
I think Iím with you all so far. Just.

If I flip a fair coin 4 times, youíre saying I could expect two consecutive tails with a probability of 1 in 4 and of two consecutive heads with a probability of 1 in 4, but I can expect two consecutive tails or two consecutive heads with a probability of 1 in 2.

Have I understood you all correctly?
yes.
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Old Mar 27, 2009, 1:18pm   #16
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TheBramble started this thread Dcraig kind of hit on what Iím driving at here.

In any series of 4 coin flips, while the probability of getting 2 consecutive heads is indeed 1 in 4 and the probability of getting 2 consecutive tails is 1 in 4, statistically, the probability of getting two consecutive tails OR two consecutive heads is 1 in 2.

But of the 16 possible permutations from a 4 coin flip, there are 12 in 16 occurrences of two consecutive Heads, and 12 in 16 occurrences of two consecutive Tails. On that basis, the probability of two consecutive Heads in a 4 coin toss exercise is 3 in 4. Same for two consecutive Tails.

So if two consecutive tails has a 3 in 4 and two consecutive heads has a 3 in 4, what it the probability of two consecutive heads OR two consecutive tails?
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Old Mar 27, 2009, 1:25pm   #17
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Tony,

Try coming at it from a different angle and determine what the chance is of not getting two heads. I know that Scripophilist is an expert in this area and he has used that approach that often gives surprising answers to probabilities.

One question that may have been posted here before but had a curios answer was:
How may people would you need to have in one room for the chances being even that two people share the same birthday ?


Paul
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Old Mar 27, 2009, 1:38pm   #18
 
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Probability Theory

is a site created by an old friend and contains interesting stuff.
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Old Mar 27, 2009, 1:40pm   #19
 
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Ah !
Just seen Paul's post.
The author of the aforementioned site is indeed Scripophilist.
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Old Mar 27, 2009, 1:52pm   #20
 
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Quote:
Originally Posted by TheBramble View Post
Dcraig kind of hit on what I’m driving at here.

In any series of 4 coin flips, while the probability of getting 2 consecutive heads is indeed 1 in 4 and the probability of getting 2 consecutive tails is 1 in 4, statistically, the probability of getting two consecutive tails OR two consecutive heads is 1 in 2.

But of the 16 possible permutations from a 4 coin flip, there are 12 in 16 occurrences of two consecutive Heads, and 12 in 16 occurrences of two consecutive Tails. On that basis, the probability of two consecutive Heads in a 4 coin toss exercise is 3 in 4. Same for two consecutive Tails.

So if two consecutive tails has a 3 in 4 and two consecutive heads has a 3 in 4, what it the probability of two consecutive heads OR two consecutive tails?
ok. still on first page, and I am now confused.

if you flip a coin 4 times, the permutations of consecutive Heads positions are: (1,2), (2,3) or (3,4).
the 4 heads in a row option gives you the above all in one go, so, say 3 again,
total 6.
but, strictly speaking, only 4 of those throws results in a 2-consec result.

dont know where you get the 12 possibilities from.

from dcraigs .75; you ask how many times would you need to throw to get a Head. If you get a Head on the first throw, you stop throwing.
You only flip the coin again if the first wasnt a Head. this negates one of dcraigs options, so we are back to 0.5.

EDIT: writing before thinking. yes, the possibility of (1,2) and (2,3) also exists, so HHHT shows 2 hits. so, yes maybe 12. havent checked it.
I was assuming finishing once you got your consec.

EDIT2: yes, there are 12 instances of consecs. (Pascals Triangle)
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# There are 10 kinds of people in the world; those that understand binary, and those that dont. -Anon
# Ed Seykotas Whipsaw Song http://www.youtube.com/watch?v=LiE1V...Wlxk8&index=10
# Defeat is temporary. Giving up makes it permanent. Anon

Last edited by trendie; Mar 27, 2009 at 2:03pm.
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