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

Algebra ->  Probability-and-statistics -> 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      Log On


   

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) About Me  (Show Source):
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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
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Cheers,
Stan H.