SOLUTION: A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jel

Question 315863: A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jelly bean is red.
What is the probability that it came from the first bag?
(Bayes's theorem)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A bag contains 4 red and 2 green jelly beans, the second bag contains 2 red and 3 green jelly beans. A bag is selected at random and a jelly bean is randomly taken from it. The jelly bean is red.
What is the probability that it came from the first bag?
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P(1st|red) = P(1st and red)/P(red)
= [P(red|1st)*P(1st)]/[P(red and 1st + P(red and 2nd)]
= [(4/6)*(1/2)]/[(4/6)*(1/2) + (2/5)(1/2)]
= [(1/3)/[(1/3)+(1/5)]
= (1/3)/(8/15)
= 5/8
==============
Cheers,
Stan H.
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