Please use D2L to turn in both the HTML output and your R Markdown file in.

### Q1. (10 pts)

Use a dataset containing homes in the Seattle, WA area http://www.math.montana.edu/ahoegh/teaching/stat408/datasets/SeattleHousing.csv for this question.

#### a. (4 points)

Create a two-by-two table containing bathrooms (grouped as: 0 - 2, more than 2 - 4, more than 4) and bedrooms (0, 1-2, 3-4, 5 or more).

#### b. (2 points)

Compute marginal probability of having 0 - 2 bathrooms

#### c. (2 points)

Compute marginal probability of having 0 - 2 bathrooms, given a house has 3-4 bedrooms

#### d. (2 points)

Are bathrooms and bedrooms indepedent? Why or why not.

### Q2. (10 pts)

Following the outline from class, assume you create a new independent test for ESP, that also has a hit rate of 9999 / 10,000, but the false detection rate is 1 in 100,000 (not 10,000).

#### a. (6 pts)

If a person tests positive for ESP using your test, what is the probability that they can perform ESP?

#### b. (4 pts)

Assume a person is given both ESP tests (the new one described above and the one outlined in class) and that the outcome of those tests is independent. If this person tests positive with both tests, what is the probability that they can perform ESP?