## Problem Description:

The following probability assignment solutions are based on probability calculations and the interpretation of relative risk. In each case, we are presented with a contingency table that contains fictitious data from various studies. The goal is to determine and interpret the relative risk, which measures the likelihood of an event occurring in one group compared to another. Relative risk is used to assess the effectiveness of treatments, habits, or behaviors and their impact on outcomes.

## 1. Assessing the Effectiveness of a New Drug

**Scenario: **In this scenario, we examine the results of a medical study designed to evaluate a new drug's ability to reduce deaths. Two groups received either the new drug or a placebo, and we aim to calculate the relative risk of a patient dying in each group.

**Solution: **The relative risk is calculated by comparing the probability of a patient dying in the new drug group to the placebo group.

- Probability of a patient dying in the new drug group: 15/150 = 0.1Probability of a patient dying in the placebo group: 36/180 = 0.2

Therefore, the relative risk is 0.1/0.2 = 0.5. This indicates that patients who received the new drug are 0.5 times less likely to die compared to those who received the placebo. In other words, the new drug reduces the risk of patient mortality.

## 2. Assessing Cell Phone Use while Driving

**Scenario:** In this scenario, we investigate the habits of automobile drivers in relation to cell phone use and age. We want to calculate and interpret the relative risk of drivers under 50 using a cell phone while driving compared to those 50 or older.

**Solution:** To calculate the relative risk, we compare the probability of drivers under 50 using a cell phone while driving to drivers aged 50 or older.

- Probability of drivers under 50 using a cell phone while driving: 240/255 = 0.941
- Probability of drivers aged 50 or older using a cell phone while driving: 30/240 = 0.125

The relative risk is 0.941/0.125 = 7.53. This indicates that drivers under 50 years of age are 7.53 times more likely to use a cell phone while driving on the highway compared to drivers aged 50 or older. Therefore, younger drivers are at a significantly higher risk of using a cell phone while driving.

## 3. Assessing the Effectiveness of a Flu Vaccine

**Scenario:** In this scenario, we analyze the results of an epidemiology study assessing the effectiveness of a flu vaccine. We aim to calculate and interpret the relative risk of a person developing the flu after receiving the vaccine compared to those who did not.

**Solution:** The relative risk is calculated by comparing the probability of a person developing the flu after receiving the vaccine to those who did not.

- Probability of a person developing the flu after receiving the vaccine: 12/100 = 0.12
- Probability of a person developing the flu without receiving the vaccine: 45/130 = 0.346

The relative risk is 0.12/0.346 = 0.35. This suggests that those who received the flu vaccine are 0.35 times less likely to get the flu compared to those who did not receive the vaccine. In other words, the vaccine reduces the risk of flu.

## 4. Assessing Flight School Dropouts by Gender

**Scenario:** In this scenario, we examine the results of a survey conducted by a Part 61 flight school to assess gender differences in dropout tendencies. We aim to calculate and interpret the relative risk of females dropping out of flight school compared to males.

**Solution: **The relative risk is calculated by comparing the probability of a female student dropping out of flight school with high and low dropout tendencies.

- Probability of a female student dropping out with high dropout tendency: 120/195 = 0.615
- Probability of a female student dropping out with low dropout tendency: 80/205 = 0.390

The relative risk is 0.615/0.390 = 1.58. This implies that female students with a high dropout tendency are 1.58 times more likely to drop out of flight school compared to female students with a low dropout tendency. In summary, female students with a high tendency are at a greater risk of dropping out.