Basic Probability

TheBramble · Mar 27, 2009, 5:34am

Quote:

Originally Posted by dcraig1

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?

TheHoneyMonster · Mar 27, 2009, 5:39am

Quote:

Originally Posted by TheBramble

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.

TheBramble · Mar 27, 2009, 5:45am

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 I’m sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that I’d 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?

TheHoneyMonster · Mar 27, 2009, 5:55am

Quote:

Originally Posted by TheBramble

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 I’m sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that I’d 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.

trendie · Mar 27, 2009, 6:06am

yes. as per THM.

TheBramble · Mar 27, 2009, 6:08am

I think I’m with you all so far. Just.

If I flip a fair coin 4 times, you’re 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?

trendie · Mar 27, 2009, 6:14am

Quote:

Originally Posted by TheBramble

I think I’m with you all so far. Just.

If I flip a fair coin 4 times, you’re 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.

TheBramble · Mar 27, 2009, 7:18am

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?

Mar 27, 2009, 5:45am	#11
TheBramble Banned Member Since Jul 2003 8,434 Posts	Re: Basic Probability 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 I’m sure you are, that the probability of getting two consecutive heads is 1 in 4, this would imply that I’d 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?

Mar 27, 2009, 6:06am	#13
trendie Legendary Member Member Since Jan 2004 5,683 Posts	Re: Basic Probability yes. as per THM. __________________ # If the only tool you have is a hammer, you tend to see every problem as a nail - Abraham Maslow # 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

Mar 27, 2009, 6:08am	#14
TheBramble Banned Member Since Jul 2003 8,434 Posts	Re: Basic Probability I think I’m with you all so far. Just. If I flip a fair coin 4 times, you’re 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?

Mar 27, 2009, 7:18am	#16
TheBramble Banned Member Since Jul 2003 8,434 Posts	Re: Basic Probability 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?

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