perplexus.info :: Probability : Known and Unknown Balls

Known and Unknown Balls (Posted on 2010-05-19)

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Not enough information

| Comment 1 of 4

Without an a priori distribution for the distribution of blue balls, there is not a definite way to calculate the probability.

Presumably, we are expected to assume a priori that all values of blue balls between 0 and 6 are equally likely, but this is just an assumption.

After the draw, the number of blue balls are known to be between 3 and 6, but the bayesian probability distribution is no longer equally likely (unless the a priori distribution is very odd).

Posted by Steve Herman on 2010-05-19 12:04:12

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