a large dam is being planned , and the engineer is interested in the source of the aggregate for the concrete. a likely source near the site is tather difficult to survey accurately. from surface indications and a single test pit, the engineer believes that the magnitude of the source has the possible descriptions: 50 percent adequate; or 150 percent of possible demand. he assigns the following probabilities of these states.

State______________________________________Probability

50% ______________________________________ 0.5

Adequate__________________________________ 0.4

150% of demand_____________________________ 0.1

___

1.0

Prior to ordering a second test pit, the engineer decides that the various likelihoods of the sample's possibility indications (Z1, Z2, Z3) depends upon the (Unknown)

P(sample of the indication state

50% _____Adequate _____ 150%

z1, favoring 50% 0.5 _______ 0.40 ______0.20

z2, favoring adequate 0.40 ______ 0.50 _______0.40

z3, favoring 150% 0.10 ______ 0.10 ________ 0.4

____ ____ ____

1.00 1.00 1.00

What are the probabilities of observing the various event z1, z2, z3, ?

The second test pit is dug and the source appears adequate from this pit.

Compute the posterior probabilities of state. If another test pit gives the same result, calculate the second set of posterior state probabilities. Compare prior and posterior state probabilities.