COU 1: Modeling Conditional Probability
Imagine an election in which two persons named Abel and Boaz are running as candidates. Suppose Abel is uncertain about whether or not a third person named Chantelle will also enter the race as a third candidate. Moreover, Abel knows that his chances of winning the election depend on whether Chantelle enters the race.
Prompt 1
Write a probabilistic model depicting Abel’s uncertainty about two issues:
- Whether Chantelle will enter the race.
- Whether Abel will win the election.
Construct the model so that the probability that Abel wins the race is conditional on whether Chantelle enters as a candidate. Specifically, the likelihood that Abel wins should be lower if Chantelle enters than if Chantelle does not enter. Specify all probabilities in the model as specific numerical values, not as expressions of parameters.
Prompt 2
Write a probabilistic model depicting Abel’s uncertainty about two issues:
- Whether Chantelle will enter the race.
- Whether Abel will win the election.
Construct the model so that the probability that Abel wins the race is conditional on whether Chantelle enters as a candidate. Specifically, the likelihood that Abel wins should be higher if Chantelle enters than if Chantelle does not enter. Specify all probabilities in the model as specific numerical values, not as expressions of parameters.
Rubric
A probabilistic model of the kind required by Prompts 1 and 2 will first specify a probability distribution over the event that Chantelle enters the race like this…
| Event | Probability |
|---|---|
| Chantelle enters | |
| Chantelle does not enter |
…with specific numerical probabilities written in the second column, and then will specify distributions over whether Abel wins that are conditional on Chantelle’s entry like this:
| Outcome | Probability |
|---|---|
| Abel wins the election | |
| Abel does not win the election |
| Outcome | Probability |
|---|---|
| Abel wins the election | |
| Abel does not win the election |
You get up to 2 points on your response to each prompt – 1 point if you respond with valid probability distributions structured as above and another 1 point if the numerical probabilities you assign are ordered relative to one another as required in the relevant prompt.