Basic Probability

This is a discussion on Basic Probability within the The Foyer forums, part of the Off the Grid category; Originally Posted by dcraig1 Possible outcomes: H H H T T H T T => probability of at least one ...

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Old Mar 27, 2009, 10:34am   #9
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TheBramble started this thread
Quote:
Originally Posted by dcraig1 View Post
Possible outcomes:

H H
H T
T H
T T

=> probability of at least one head is 0.75, because all outcomes are equally likely.
No, I meant as a separate exercise. If I flip a fair coin twice, I should expect a head, statistically, as the probability of flipping a head on any one coin toss is 1 in 2. Is that correct?
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Old Mar 27, 2009, 10:39am   #10
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Originally Posted by TheBramble View Post
OK. Right.

So the chance of my flipping a Head on any one toss of the coin is 50% or 1 in 2. Which means, I’d need to flip the coin twice to, statistically, expect to get a head. Is that correct?
Yes, statistically. Try flipping a coin 100 times and I'd be surprised if the split was more exagerrated than 55/45after 100. During this 100 flips there will probably be runs of 4-5 consecutive heads or tails, and heads or tails may seem to build a lead, but by the "end" of the sample, things pretty much equate.
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Old Mar 27, 2009, 10:45am   #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, 10:55am   #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, 11:06am   #13
 
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yes. as per THM.
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Old Mar 27, 2009, 11:08am   #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, 11:14am   #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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# 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
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Old Mar 27, 2009, 12:18pm   #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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