(no subject)
Sep. 22nd, 2005 08:50 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
which_chickFrom the brother's blog:
Assume you have in you pocket three coins. One of these coins has two heads. (1)What is the probability of removing one coin, flipping it once and having it land with a heads result? (2)What is the probability that this coin is the false coin? (3)What are these percentages if you flip the same coin again? (4)Can you know for certain if the coin you are flipping is the fake and how?
1. The probability of removing one coin, flipping it once, and having it land with a heads result is 2 in 3, or .6666(etc)
This is because our viable options here are H, T, H, T, H, H. That's six choices, two tails and four heads. Odds of heads are 2 in 3 or .6666
2. The probability that this coin is the false coin is a conditional probability. GIVEN that we got heads on the first toss, what are the odds that this hyar is the false coin?
There are four shots at getting heads (this is the reduced sample space -- for conditional probablity you generate a reduced sample space from the results of the first condition to use for the second condition) and of the four shots at getting heads, two of them are given by the fake coin. Thus, the probability that this is the fake coin is 1 in 2 or .5
3. What are these percentages if you flip the same coin again?
The viable options expand for flipping the coin again.
H H
H T
T T
T H
(end of coin 1)
H H
H T
T T
T H
(end of coin 2)
H H
H H
H H
H H
(end of fake coin 3)
The odds for flipping the same coin again and again getting heads are 6 in 12 or .5 (and the odds for 'flip the coin again and get heads yet again' should drop as you do more flips, even if you have one-of-three and there's a fake coin in the set of three that you drew from)
The odds that THIS COIN is the fake coin, this one that's given you heads twice in a row, now, are 4 in 6 or .6666 (etc). (and the odds for 'given that THIS COIN which keeps giving you heads is the coin where both faces are heads' should go up as you do more flips.)
4. Can you know for certain if the coin you are flipping is the fake one? Hell yes. How? Turn it over and over in your hand and fucking look at it, what, are you stupid? Other than that, no. You cannot know for certain. You can do probablity and you can do confidence intervals and that sort of statistical goodness is frequently good enough to be getting on with... but if you want to KNOW FOR CERTAIN if you have the fake coin, you best turn it over in your fucking hand and look at it.
Do I get extra melons?
Assume you have in you pocket three coins. One of these coins has two heads. (1)What is the probability of removing one coin, flipping it once and having it land with a heads result? (2)What is the probability that this coin is the false coin? (3)What are these percentages if you flip the same coin again? (4)Can you know for certain if the coin you are flipping is the fake and how?
1. The probability of removing one coin, flipping it once, and having it land with a heads result is 2 in 3, or .6666(etc)
This is because our viable options here are H, T, H, T, H, H. That's six choices, two tails and four heads. Odds of heads are 2 in 3 or .6666
2. The probability that this coin is the false coin is a conditional probability. GIVEN that we got heads on the first toss, what are the odds that this hyar is the false coin?
There are four shots at getting heads (this is the reduced sample space -- for conditional probablity you generate a reduced sample space from the results of the first condition to use for the second condition) and of the four shots at getting heads, two of them are given by the fake coin. Thus, the probability that this is the fake coin is 1 in 2 or .5
3. What are these percentages if you flip the same coin again?
The viable options expand for flipping the coin again.
H H
H T
T T
T H
(end of coin 1)
H H
H T
T T
T H
(end of coin 2)
H H
H H
H H
H H
(end of fake coin 3)
The odds for flipping the same coin again and again getting heads are 6 in 12 or .5 (and the odds for 'flip the coin again and get heads yet again' should drop as you do more flips, even if you have one-of-three and there's a fake coin in the set of three that you drew from)
The odds that THIS COIN is the fake coin, this one that's given you heads twice in a row, now, are 4 in 6 or .6666 (etc). (and the odds for 'given that THIS COIN which keeps giving you heads is the coin where both faces are heads' should go up as you do more flips.)
4. Can you know for certain if the coin you are flipping is the fake one? Hell yes. How? Turn it over and over in your hand and fucking look at it, what, are you stupid? Other than that, no. You cannot know for certain. You can do probablity and you can do confidence intervals and that sort of statistical goodness is frequently good enough to be getting on with... but if you want to KNOW FOR CERTAIN if you have the fake coin, you best turn it over in your fucking hand and look at it.
Do I get extra melons?
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no subject
Date: 2005-09-24 02:11 pm (UTC)2. I assume that "this coin" is the coin you flipped for a heads result. P(false) = P(false & heads) / P(heads) = (1/3 * 1) / (2/3) = 1/2.
3. The probability that the coin will show heads again is P(fair) * 1/2 + P(false) * 1 = 1/2 * 1/2 + 1/2 = 3/4. The probability that the coin is the false coin hasn't changed. However, if the coin shows tails, we'll know it's not the false coin, and the probability of tails is P(fair) * 1/2 = 1/2 * 1/2 = 1/4.
4. YES, WITHOUT PEEKING!!! Take the other two coins out of your pocket and start flipping all three. Eventually, two of them will have shown tails, and you'll know that the third coin is the false one. Since the probability that a fair coin will never have landed on tails goes to zero as the number of flips increases, this method is guaranteed to eventually yield an answer, and the answer will be 100% certain!
no subject
Date: 2005-09-24 05:01 pm (UTC)