A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Refer to the following payoff table:

 

  State of Nature
Alternative S1 S2
A1 75 −40
A2 0 100
Prior Probability 0.6 0.4

 

There is an option of paying $100 to have research done to better predict which state of nature will occur. When the true state of nature is S1, the research will accurately predict S1 60% of the time. When the true state of nature is S2, the research will accurately predict S2 80% of the time.

 

What is the unconditional probability that the research predicts S1?

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There is an option of paying $100 to have research conducted to better predict which state of nature will occur. When the true state of nature is High, the research will accurately predict High 70% of the time. When the true state of nature is Low, the research will accurately predict Low 75% of the time.

Given that the research is conducted, what is the joint probability that the state of nature is High and the research predicts Low?

 

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There is an option of paying $100 to have research conducted to better predict which state of nature will occur. When the true state of nature is High, the research will accurately predict High 70% of the time. When the true state of nature is Low, the research will accurately predict Low 75% of the time.

Given that the research is conducted, what is the joint probability that the state of nature is High and the research predicts Low?

 

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