Originally posted by PalynkaI was simply describing what was needed for the most complex method of analysing the problem I know of.
A binomial test doesn't require any such assumption.
Of course, there was in the original problem an implicit assumption the coin was fair. In such a case, one need only realize that a fair coin has no memory of past events, and we are only discussing a single flip.
Someone else brought up a "one of two coins" scenario which has a very different answer, and a more complex working out.
Originally posted by wolfgang5950%......the "test" ie the three coin flips won't change the fact that you are starting with two coins one of which is double headed
You have 2 coins; one is a normal, fair coin, the other is double-headed.
You randomly pick one of the coins and pass to a friend who flips it three times noting the result.
If the result is HHH what is the probability the coin is fair?
Originally posted by shrewIt does, because it provides you with information about the coin your friend is holding. The additional information comes from the fact that it's more likely for the double headed to give you HHH than a normal one.
50%......the "test" ie the three coin flips won't change the fact that you are starting with two coins one of which is double headed
If you still have doubts, think about what would happen if you had gotten at least one tail. Then you could be 100% certain that the coin you're testing is not double head.
Alternatively, think what would happen if you did 10000000000 flips and gotten all heads. Would you still argue that the chance that the coin is double headed is 50%? Every throw gives you some information.
One tail will prove the case but no matter how many heads you throw how can you be certain.You are still making the original choice of one coin from two.The more tests you perform it becomes more likely that you can state which coin you have got (without the true test of looking at both sides) but will it change the starting probabilty?
Originally posted by shrewThe question is not the unconditional ex-ante probability, but what is the probability conditional on the result of the three throws.
One tail will prove the case but no matter how many heads you throw how can you be certain.You are still making the original choice of one coin from two.The more tests you perform it becomes more likely that you can state which coin you have got (without the true test of looking at both sides) but will it change the starting probabilty?
How will flipping three heads in a row increase the probabilty that you have the double headed coin...its still a choice of one from a group of two.The "test" only increases the chance that you can make a correct prediction. Flipping the coin dos'nt change the probabilty of the coin being double headed or not.
Originally posted by shrewDo you even know what probability is?
How will flipping three heads in a row increase the probabilty that you have the double headed coin...its still a choice of one from a group of two.The "test" only increases the chance that you can make a correct prediction. Flipping the coin dos'nt change the probabilty of the coin being double headed or not.
Either the coin is the one or it isn't. That never changes and has little to do with probability. In this case, probability is just a measure of likelihood conditional on the information you have. So, yes, having information about the three throws changes the value of the probability by changing the information on which probability is conditional on.
The probabilty of the double headed coin showing HHH is one.
The probabilty of the true coin showing HHH is 1/8.
The "test" suggests that I have the double headed coin but it is nowhere near 100% certain......the original chance of selecting the double headed coin is still 1/2.
Originally posted by shrewAnd? Do you remember what the question was?
The probabilty of the double headed coin showing HHH is one.
The probabilty of the true coin showing HHH is 1/8.
The "test" suggests that I have the double headed coin but it is nowhere near 100% certain......the original chance of selecting the double headed coin is still 1/2.
Originally posted by PalynkaAs you say"either the coin is is'nt". The probabilty has'nt changed from the outset how can it?The "odds" have changed.How many tests with a result of heads would you need to be 100% certain that you have the double headed coin?
And? Do you remember what the question was?