## **Core Concept**
The Odds Ratio (OR) is a measure used in statistics to quantify the strength and direction of the association between an exposure (in this case, smoking) and an outcome (developing a disease). It is commonly used in case-control studies but can also be applied to cohort studies as shown here. The formula to calculate the Odds Ratio in this context is: OR = (a/b) / (c/d), where a = number of exposed individuals with the disease, b = number of exposed individuals without the disease, c = number of non-exposed individuals with the disease, and d = number of non-exposed individuals without the disease.

## **Why the Correct Answer is Right**
Given the data: a = 30 (smokers with disease), b = 20 (smokers without disease, since 50 - 30 = 20), c = 10 (non-smokers with disease), and d = 40 (non-smokers without disease, since 50 - 10 = 40), we can substitute these values into the Odds Ratio formula. So, OR = (30/20) / (10/40) = (1.5) / (0.25) = 6. This means that smokers are 6 times more likely to develop the disease compared to non-smokers.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option suggests an Odds Ratio of , which does not match our calculated value of 6. Without calculating, we know this is incorrect based on our derivation.
- **Option B:** Similarly, this option does not align with our calculation.
- **Option D:** This option also does not match our calculated Odds Ratio.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that an Odds Ratio of 1 indicates no association between the exposure and the outcome. An OR greater than 1 suggests an increased risk, while an OR less than 1 suggests a protective effect. In this case, an OR of 6 indicates a strong association between smoking and the development of the disease.

## **Correct Answer:** C. 6