Question

a professor was considering whether to go for the final interview for a job. but he was going to be far away, and the flight would cost him $3,000. he would have a 2 out of 5 chance of getting the job and they pay would be $40,000 more than he is currently earning. should he go for it? what is the expected value?

Explanation:

Step1: Calculate the expected gain from getting the job

The probability of getting the job \( P(\text{get job})=\frac{2}{5}\), and the gain if he gets the job is \( G = 40000\) dollars. So the contribution to the expected value from getting the job is \(P(\text{get job})\times G=\frac{2}{5}\times40000\)

$$ \frac{2}{5}\times40000 = 16000 $$

Step2: Calculate the expected loss from not getting the job

The probability of not getting the job \(P(\text{not get job})=1 - \frac{2}{5}=\frac{3}{5}\), and the loss (cost of flight) if he doesn't get the job is \(L=- 3000\) dollars. So the contribution to the expected value from not getting the job is \(P(\text{not get job})\times L=\frac{3}{5}\times(-3000)\)

$$ \frac{3}{5}\times(- 3000)=-1800 $$

Step3: Calculate the expected value

The expected value \(EV\) is the sum of the contributions from getting and not getting the job. \(EV=\frac{2}{5}\times40000+\frac{3}{5}\times(-3000)\)

$$ EV = 16000-1800=14200 $$

Since the expected value \(EV = 14200>0\), he should go for the interview.

Answer:

The expected value is \(14200\) dollars, and he should go for the interview.