#1




question about probability
If an urn contains 100 green or red marbles, and you sample 10 and they are all green, what is the probability that they are all green?

#2




Re: question about probability
Quote:
Put it to the simplest case, if you flip a coin and get a head, what is the head probability of the coin? The answer can be "any nonzero number" but there is no further information to pin it down. Hope this helps.
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#3




Re: question about probability
Quote:
Do these help? Read through the second one for a similar example. http://badmomgoodmom.blogspot.com/20...rtone_16.html http://badmomgoodmom.blogspot.com/20...parttwo.html 
#4




Re: question about probability
Does the Hoeffding Inequality allow us to say something about this probability?
P[Ein  Eout > epsilon] <= 2e^(2 * epslion^2 * N) Since Ein = 0, N = 10, setting epsilon to 0.5, the inequality gives us: P[Eout > 0.5] <= 2e^(5) = 0.013+ This seems to be saying something nontrivial about Eout. 
#5




Re: question about probability
Quote:
The question that got answered by Hoeffding is roughly "What is the probability of a bigEout urn (many red) for generating such an Ein (all green)?" not "What is the probability of Eout being small in the first place?" The answer to the latter question remains unknown, but even so, we know that having a big Eout is unlikely because of Hoeffding. Hope this helps.
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#6




Re: question about probability
I would think this way:
if p is probability of the outcome then for 10 trials there is p^10 probability of getting all favorable outcome. 
#7




Re: question about probability
Hoeffding's inequality has a free parameter in your question, namely . It lest you say that since you have 10 samples, if you want to be 80% sure of the distribution of marbles in the jar (), then the jar is at most percent different from the sample.
where substituting from your example: simplifying: so we think that with 80% confidence, the jar is at least 10.2% green. We probably need a bigger N! 
#8




Re: question about probability
In the second lecture, the Professor asked a question about flipping a coin:
What is the probability of getting all ten heads if you flip a coin 10 times count the number of heads, and then you repeat the experiment 1000 times. The answer he gave was 63%  I would like to know how this was computed. Any help would be greatly appreciated. Thanks! 
#9




Re: question about probability
Quote:
Therefore, the probability of not getting 10 heads for one coin is approximately . This means that the probability of not getting 10 heads for any of 1000 coins is this number multiplied by itself 1000 times, once for every coin. This probability is therefore . This is approximately since . Numerically, . Therefore, the probability of this not happening, namely that at least one coin of the 1000 coins will give 10 heads, is 1 minus that. This gives us the answer of approximately 0.63 or 63% that I mentioned in the lecture.
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#10




Re: question about probability
Thank you Professor, that was extremely helpful.

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marble, probability, urn 
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