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%

-*What is the expected value at node B?
A)18.60
B)16.04
C)13.76
D)12.50

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%
 
-*What is the expected value at node B?
A)18.60 
B)16.04 
C)13.76 
D)12.50

Quizplus · Accepted Answer

The expected value at node B is calculated as follows:
E(B) = (0.30*0.58*0.16)+(0.30*0.42*0.50)+(0.70*0.58*0.84)+(0.70=0.42*0.50)= 0.096+0.063+0.290+0.147= 0.596
Therefore, the expected value at node B is 0.596 or 16.04 when rounded to two decimal places.

Answer: Choose Event B
 
At node A, the probability of Event B (0.70) is higher than the probability of Event A (0.30). 
At node B, the expected value of Event B is higher (16.04) than the expected value of Event A (13.76). Therefore, the best choice is to choose Event B. The expected value at node B can be calculated by multiplying the probabilities and payoffs for each decision, and then summing those values.

For Decision 1 under Event A: 
Expected value = (0.16 * $10) + (0.84 * $4) = $4.56

For Decision 1 under Event B: 
Expected value = (0.50 * $8) + (0.50 * $6) = $7

Therefore, the expected value at node B is: 
Expected value = (0.30 * $4.56) + (0.70 * $7) = $6.52

Based on this calculation, Decision 1 under Event B is the best choice, as it has the highest expected value of $7.

Answer: 1B 
 The best choice is Decision 1 under Event B, as it has the highest expected value of $7. Decision 1 under Event A has a lower expected value of $4.56. Decision 2 does not have a higher expected value than either of these choices.