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Known and Unknown Balls (Posted on 2010-05-19) Difficulty: 2 of 5
An urn contains 6 green balls and an unknown number, which is ≤ 6, of blue balls. Three balls are drawn successively at random, and not replaced and are all found to be blue.

Determine the probability that a green ball will be drawn at the next draw.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts Posterior probabilities Comment 4 of 4 |
I concur with Charlie's analysis.

Just to be clear,

(a) Bayesian analysis can be applied with any a priori distribution, not just uniform

(b) Nothing better than a uniform priori probability distribution is available.  In other words, a priori
    blue probability
    0      1/7
    1      1/7
    2      1/7
    3      1/7
    4      1/7
    5      1/7
    6      1/7
 (c) Then the posterior probability distribution is P(T)/Total of all P(T)'s, which calculates to approximately:
    3   6.05%
    4 16.94%
    5 30.80%
    6 46.20%

  Posted by Steve Herman on 2010-05-20 10:00:38
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