The dean of a college wants to determine which of two new classes to offer for the upcoming semester. Due to facility constraints only one class can be offered at this time. The dean feels that the first class has an 80 percent chance of earning the college about $75,000, but a 20 percent chance of losing $35,000. If the class is successful, then its next level class will be offered, with a 75 percent chance of earning $60,000, but a 25 percent chance of losing $30,000. Weighing the options, the dean feels that the second class has a 60 percent chance of earning $85,000, but a 40 percent chance of losing $40,000. If the second class is successful, then its next level class will be offered with a 50 percent chance of earning $80,000, but a 50 percent chance of losing $45,000. If both classes are not successful, neither of their next level classes will be offered to the students.What is the expected value for selecting the second class?
A)$90,000
B)$83,000
C)$75,500
D)$50,000
E)$45,500

Question

Quizplus · Accepted Answer

The expected value (EV) for selecting the second class can be calculated as follows:First, calculate the expected value of the second class itself:$$EV_{\text{second class}} = (0.60 \times \$85,000) + (0.40 \times -\$40,000) = \$51,000 - \$16,000 = \$35,000$$Then, calculate the expected value of the next level of the second class, given that the second class is successful:$$EV_{\text{next level of second class}} = (0.50 \times \$80,000) + (0.50 \times -\$45,000) = \$40,000 - \$22,500 = \$17,500$$However, the next level class is only offered if the second class is successful, which has a 60% chance. So, the expected value of offering the next level class, factoring in the probability of the second class being successful, is:$$0.60 \times \$17,500 = \$10,500$$Finally, add the expected values of the second class and its next level class together:$$EV_{\text{total for second class}} = \$35,000 + \$10,500 = \$45,500$$Therefore, the expected value for selecting the second class is \$45,500.

The Dean of a College Wants to Determine Which of Two