Question

Urn A has 1 red and 2 black balls. Urn B has 2 red and 1 black ball. It is common knowledge that nature chooses both urns with equal probability, so P(A)=0.5 and P(B)=0.5. A sequence of six balls is drawn with replacement from one of the urns. Experimental subjects do not know which urn the balls are drawn from. Let x denote the number of red balls that come up in the sample of 6 balls, x=0,1,2,...,6. Suppose that the sample, based on six draws, turns out to be x=2. What is the posterior probability based on Bayes' law that the sample came from urn A?

	A.	0.71
	B.	0.80
	C.	0.65
	D.	0.76

Answer 1