Please solve the question by Bayes theorem?

Question

There are three urns containing black, red and green balls. urn 1 contains 4 black, 5 red and 3 green balls urn 2 contains 7 black, 4 red and 4 green balls urn three contains 6 black, 6 red and 5 green balls. An urn is chosen and ball is picked if the ball picked is green find the probability it has come from urn 3.

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Answer 1 · 2017-12-01T17:35:02

$300 / 827$

$P[ "Urn 3|Green" ] P[ "Green" ] = P[ "Green|Urn 3" ] P[ "Urn 3" ]$

$=> P[ "Urn 3|Green" ] = (P[ "Green|Urn 3" ] P[ "Urn 3" ]) / (P[ "Green" ])$

$= ((5/17) (1/3)) / [ ((3/12) + (4/15) + (5/17))/3 ]$

$= (5/17) / [ 3/12 + 4/15 + 5/17 ]$

$= 5 / [ 51/12 + 68/15 + 5 ]$

$= 5 / [ (255 + 272 + 300 ) / 60 ]$

$= 300 / 827$