Instructor Katherine Cliff
Warm Up Questions
The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) conditional on whether or not they have health insurance.
| Excellent | Very Good | Good | Fair | Poor | |
|---|---|---|---|---|---|
| No Coverage | 0.023 | 0.0364 | 0.0427 | 0.0192 | 0.005 |
| Coverage | 0.2099 | 0.3123 | 0.241 | 0.0817 | 0.0289 |
A. Are being in excellent health and having health coverage mutually exclusive? Explain.
Warm Up Questions
The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) conditional on whether or not they have health insurance.
| Excellent | Very Good | Good | Fair | Poor | |
|---|---|---|---|---|---|
| No Coverage | 0.023 | 0.0364 | 0.0427 | 0.0192 | 0.005 |
| Coverage | 0.2099 | 0.3123 | 0.241 | 0.0817 | 0.0289 |
B. What is the probability that a randomly chose individual has excellent health?
Warm Up Questions
The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) conditional on whether or not they have health insurance.
| Excellent | Very Good | Good | Fair | Poor | |
|---|---|---|---|---|---|
| No Coverage | 0.023 | 0.0364 | 0.0427 | 0.0192 | 0.005 |
| Coverage | 0.2099 | 0.3123 | 0.241 | 0.0817 | 0.0289 |
C. What is the probability that a randomly chosen individual has excellent health given that he has no health coverage?
Warm Up Questions
The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) conditional on whether or not they have health insurance.
| Excellent | Very Good | Good | Fair | Poor | |
|---|---|---|---|---|---|
| No Coverage | 0.023 | 0.0364 | 0.0427 | 0.0192 | 0.005 |
| Coverage | 0.2099 | 0.3123 | 0.241 | 0.0817 | 0.0289 |
D. What is the probability that a randomly chosen individual has excellent health given that he has no health coverage?
Warm Up Questions
The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table displays the distribution of health status of respondents to this survey (excellent, very good, good, fair, poor) conditional on whether or not they have health insurance.
| Excellent | Very Good | Good | Fair | Poor | |
|---|---|---|---|---|---|
| No Coverage | 0.023 | 0.0364 | 0.0427 | 0.0192 | 0.005 |
| Coverage | 0.2099 | 0.3123 | 0.241 | 0.0817 | 0.0289 |
E. Does having excellent health and having health coverage appear to be independent? Use your answers above to justify your response.
Even More Warm up
Suppose 80% of people like peanut butter, 92% like jelly, and 77% like both. Given that a randomly sampled person likes peanut butter, what’s the probability that they also like jelly?
Last Warm up
Given that P(A)=0.31, P(B)=0.59, and P(A and B) = 0.10, find P(not B | A).
Selecting items from a set with replacement
Example 1
Three cards are drawn from a standard deck with replacement, shuffling after each draw. What is the probability that we draw an ace, then a two, and then a three?
Selecting items from a set without replacement
Example 2
Three cards are drawn from a standard deck without replacement. What is the probability that we draw an ace, then a two, and then a three?
Example 3
Three cards are drawn from a standard deck without replacement. What is the probability that we draw an ace, then a two, and a three in any order?
You try
What is the probability of being dealt (without replacement) the following hand from a well shuffled full deck: first a red card, then a spade, and lastly the ace of hearts?
You try
What is the probability of being dealt (without replacement) the following hand from a well shuffled full deck: a red card, a spade, and the ace of hearts IN ANY ORDER?
Baye’s Rule
Example 4:
Company A supplies 40% of the computers sold and is late 5% of the time. Company B supplies 30% of the computers sold and is late 3% of the time. Company C supplies another 30% and is late 2.5% of the time. A computer arrives late - what is the probability that it came from Company A?
Work on numbers 6-8
In Canada, about 0.35% of women over 40 will develop breast cancer in any given year. A common screening test for cancer is the mammogram, but this test is not perfect. In about 11% of patients with breast cancer, the test gives a false negative. Similarly, the test gives a false positive in 7% of patients who do not have breast cancer. If we tested a random woman over 40 for breast cancer using a mammogram and the test came back positive, what is the probability that the patient actually has breast cancer?
Textbook prices and conditions have a seasonality structure on Ebay. The market is most active in the two-week windows at the beginning and end of terms as sellers provide a large quantity of books for students to purchase and then students sell their textbooks after finals. Suppose we consider a particular physics textbook that commonly sells on Ebay, and we find that about 38% of this textbook’s sales occur at the beginning of a term, and about 70% of these start-of-term textbook sales are for new books. Suppose end-of-term book sales make up about 22% of this book’s sales on Ebay, 89% of which are used books. Then the remainder of the books sold on Ebay are outside of the beginning and end-of-term periods, where about 47% of books sold are new. Suppose we randomly sample one of these physics textbook from Ebay’s database and we know the book is used. Then what is the probability the book was sold at the start of a term? (Be sure to answer in a proportion, not a percentage.)
On the old game show “Let’s Make a Deal”, the host, Monty Hall presents to you three doors. Behind one of the doors is a brand new car. Behind the other doors are goats. Let’s assume you want to win the car. First, you get to select a door. Next, Monty will open one of the remaining doors, behind which is a goat (Monty always reveals a goat). Then, you have the option to stick with the door you original picked, or switch doors. Are you more likely to win if you stick with your first choice, or if you switch? What are the chances of winning in each scenario? Explain your work.