Heading: Analyzing Risky Decisions
**Reference: Use the decision tree along with the given probabilities to answer the next six questions
Probability Event A = 30% Probability Event B = 70%
Probability Event 1 = 58% Probability Event 2 = 42%
Probability of Event A given that Event 1 occurs = 16%
Probability of Event B given that Event 1 occurs = 84%
Probability of Event A given that Event 2 occurs = 50%
Probability of Event B given that Event 2 occurs = 50%

-*If the decision maker chooses Decision A and Event 2 occurs, which decision alternative should the decision maker choose at node E?
A)Decision 1
B)Decision 2
C)Either Decision; they both have the same expected value.
D)Neither Decision; more information is needed.

Question

Heading: Analyzing Risky Decisions
**Reference: Use the decision tree along with the given probabilities to answer the next six questions 
Probability Event A = 30% Probability Event B = 70%
Probability Event 1 = 58% Probability Event 2 = 42%
Probability of Event A given that Event 1 occurs = 16%
Probability of Event B given that Event 1 occurs = 84%
Probability of Event A given that Event 2 occurs = 50%
Probability of Event B given that Event 2 occurs = 50%
 
-*If the decision maker chooses Decision A and Event 2 occurs, which decision alternative should the decision maker choose at node E?
A)Decision 1 
B)Decision 2 
C)Either Decision; they both have the same expected value. 
D)Neither Decision; more information is needed.

Quizplus · Accepted Answer

If Decision A is chosen and Event 2 occurs, there is a 50% chance of either Event A or Event B happening. Given that Event B has a higher probability (70%) than Event A (30%), the decision maker should choose Decision 2, which leads to a higher payoff in the event of Event B occurring. Therefore, the best choice is Decision 2 at node E. If Decision A is chosen and Event 2 occurs, the decision tree leads to node E with an expected payoff of 0.5(0) + 0.5(100) = 50. At node E, if Decision 1 is chosen, the expected payoff is 0.5(50) + 0.5(80) = 65. If Decision 2 is chosen, the expected payoff is 0.5(0) + 0.5(120) = 60. Therefore, Decision 1 has the higher expected payoff and should be chosen.