which_chick (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
which_chick) wrote2005-09-22 08:50 pm
which_chick) wrote2005-09-22 08:50 pm
(no subject)
From 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?
I'm not as shmart as you, but...
Assume you have in you pocket three coins. One of these coins has two heads.
OK.
What is the probability of removing one coin, flipping it once and having it land with a heads result?
There are 2 normal coins and on 2-headed. Normal coin is 50% chance of heads. Fake is 100% chance of heads. 1/3 of the time you will pull the fake, and it will always return heads (100% of the time), so the probability that you have a heads from it is 33%
A normal coin has a 1/3 chance of being pulled with a probable result of .5 heads and .5 tails. You have two of these, so I think the chance of heads on these two is also 33%.
.333+.333 = .666, or 2/3 of the time.
Also, in your pocket there are 4 heads and two tails, so 4/6=66.6%
What is the probability that this coin is the false coin?
It has already returned heads, so there are four heads, two of which belong to the fake coin, so the porbability is 50/50. You must exclude the tails possibilities from the odds.
What are these percentages if you flip the same coin again?
A 100% chance that my head will hurt. The percentages on the first result won't change. If the second toss results in a "tails", there is a zero percent chance that you have the fake and a 100% chance that it is a regular coin. If the second toss results in a "Heads", you have no idea what you have flipped - fake or "real", but the possiblity remains that it is heads.
If you got a "heads" the first time, then you are still dealing with 50/50 chance for a "heads" on the second throw. Your chance of getting heads twice in a row when you have a 50/50 shot should be about 1/4 assuming you are saying that the first throw has not been made and you are asking what are the chances that you'll have two consecutive heads throws without knowing any of the results ahead of time.
Can you know for certain if the coin you are flipping is the fake and how?
1. You look at both sides of all three coins.
2. If you are asking about a mechanism to determine via throwing and not peeking, then you should throw all three coins simultaneously, picking up each "tails" that you see and throwing the remaining coins. Once you've picked up two coins, the third is the fake. This could take lots and lots of throws, but, from a practical standpoint, I think it is highly likely that you'll be done in under ten tosses in virtually all circumstances. In 210 tries for flipping, the odds of 10 consecutive heads are exceptionally small -- I think 1/1024 for one coin.
You can never determine conclusively without peeking. You can get "close enough" however.
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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!
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