water quality from a specific source is believed to be good

water quality from a specific source is believed to be .good. (satisfacory) with a 95% confidence. A quick test can be performed to check the quality. The track record of this test is: 5 P(Ai Sj) Given State of Nature S1 S2 Test outcomes: A1 0.7 0.2 A2 0.3 0.8 Where S1 -the water is good, S2 the water is not good. Two samples were taken and both were tested. Both test outcomes indicate A2. What is the updated or current belief that the water is still good? (10 points)

Solution

The 2 samples taken for test can fall in either of s1 and s2 category.For the test with outcome indicating the water quality is satisfactory can have probability of 0.7 or 0.2