Suppose that the proportion θ of defective items in a large manufactured lot is known to be either 0.1 or 0.2, and the prior p.f. of θ is as follows:

Suppose also that when eight items are selected at random from the lot, it is found that exactly two of them are defective. Determine the posterior p.f. of θ.

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ξ(0.1) = 0.7 and ξ(0.2)=0.3.