Probability: Bayes theorem MCQ

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Bayes theoremHardQuestion 270013

Question

Bag I has 3 red, 4 black. Bag II has 5 red, 6 black. A bag is selected at random and a red ball is drawn. P(it came from Bag I) is:

33/68

By Bayes' theorem, $P(I|R)=[(1/2)(3/7)]/[(1/2)(3/7)+(1/2)(5/11)]=(3/7)/(3/7+5/11)=<strong>33/68</strong>$ .