This problem focuses on the option to purchase multiple sources of information with different prices. Two salesmen approach Kim: One is selling an Acme Rain Detector, and the other is selling a Beta...

This problem focuses on the option to purchase multiple sources of information with different prices. Two salesmen approach Kim: One is selling an Acme Rain Detector, and the other is selling a Beta Rain Detector. After conferring with one another, they offer Kim the following opportunities.

• Kim can buy the Acme detector (at any time) for $10.

• Kim can buy the Beta detector (at any time) for $ 13.

• Kim can buy both detectors (at the same time) for $ 16. Kim believes that the Acme detector is symmetric, and it has an accuracy of 0.8. In other words,

{"S"|5,&} = {"R"|R, &} = 0.8

where "S" is the event that the test indicates Sunny, S is the event that the weather is actually sunny (similarly for rain).