I apologize if this one already got posted, but i haven't found it through the search function. I found
this one on the Hoeflin Power Test.
Suppose you are truthfully told that ten marbles were inserted into a box, all of them identical except that their colors were determined by the toss of an unbiased coin. When heads came up, a white marble was inserted, and when tails came up, a black one. You reach into the box, draw out a marble, inspect its color, then return it to the box. You shake the box to mix the marbles randomly, and then reach in and again select a marble at random. If you inspect ten marbles in succession in this manner and all turn out to be white, what is the probability to the nearest whole percent that all ten marbles in the box are white?
I'm not sure whether I can use the following method:
We need to find the posterior probability that when we take 10 whites, there are only whites in the box.
In order to do so we need to use Bayes' theorem: P(A/B) = P(B/A)*P(A) / P(B)
=>
- P(A) = odds that there are 10 white marbles in the box
= binominal (k = 10; n = 10, p = 1/2)
- P(B/A) = odds that one picks 10 white marbles out of 10 picks out of the box when there are 10 white marbles in the box
= binominal (k = 10; n = 10, p = 1)
- P(B) = cumulative odds of picking 10 whites out of 10 picks when not known how many whites there are in the box
= sum of i = 0..10 : binominal (k = i; n = 10, p = 1/2) * binominal (k = 10; n = 10, p = i/10)
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Hi,
I apologize if this one already got posted, but i haven't found it through the search function. I found
this one on the Hoeflin Power Test.
Suppose you are truthfully told that ten marbles were inserted into a box, all of them identical except that their colors were determined by the toss of an unbiased coin. When heads came up, a white marble was inserted, and when tails came up, a black one. You reach into the box, draw out a marble, inspect its color, then return it to the box. You shake the box to mix the marbles randomly, and then reach in and again select a marble at random. If you inspect ten marbles in succession in this manner and all turn out to be white, what is the probability to the nearest whole percent that all ten marbles in the box are white?
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