A chance node on a decision tree has four possible outcomes worth $10,000, $20,0

Question

A chance node on a decision tree has four possible outcomes worth $10,000, $20,000, $30,000, and -$100,000, respectively. The probabilities of these outcomes occurring are assessed as 10%, 25%, 50%, and 15%, correspondingly. What is the expected value of this chance node? A chance node on a decision tree has four possible outcomes worth $10,000, $20,000, $30,000, and -$100,000, respectively. The probabilities of these outcomes occurring are assessed as 10%, 25%, 50%, and 15%, correspondingly. What is the expected value of this chance node?

Explanation / Answer

(are there are two questions? if two questions, the below are two answers. if not two, select one answer based on the fourth value i.e. -$100,000 or $100,000)

the expected value of the first node= 0.1*10,000+0.25*20,000+0.5*30,000+0.15*(-100,000)

= 1000+5000+15,000- 15000= $6000

the expected value of the second node= 0.1*10,000+0.25*20,000+0.5*30,000+0.15*100,000

=1000+5000+15000+15000= $36,000

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