1. Conditional Probability
Suppose the probability that a student takes Economics and Psychology is 0.09. The probability that a student takes Economics is 0.70. What is the probability that a student takes Psychology given that the student is taking Economics?
2. Bayes' Theorem
Suppose that 1% of the population has a certain genetic defect. An individual can take a test to determine whether they have the genetic defect. The chance of a positive test result given that the person actually has the genetic defect is 90%. The chance of a positive test result if the person does not have the genetic defect is 7%. If a person gets a positive test result, what are the odds they actually have the genetic defect?
3. Real Options: Decision Tree Analysis
It is the beginning of January 2014 and you have been offered the following deal to go heli-skiing. If you pick the first week in January 2015 and pay for your vacation now, you can get a week of heli-skiing for $2500. However, if you cannot ski because the helicopters cannot fly due to bad weather, there is no snow, or you get sick, you do not get a refund. There is a 40% chance that you will not be able to ski. If you wait until the last minute and go only if you know that the conditions are perfect and you are healthy, the vacation will cost $4000.
You estimate that the pleasure you get from heli-skiing is worth $6000 per week to you (if you had to pay any more than that, you would choose not to go).
(a) If your cost of capital if 8% per year, should you book ahead or wait?
(b) Draw the decision tree.
4. Financial Options
(a) What is a protective put option?
(b) What is the payoff of this option?
(c) Illustrate the payoff on a graph with stock price on the x-axis and the payoff on the y-axis.