30 out of 50 smokers and 10 out of 50 non smokers develop lung cancer. What is odd’s Ratio

**Core Concept**
The odd's ratio is a measure of association between a risk factor (smoking) and a disease (lung cancer). It estimates the likelihood of disease occurrence in the presence of the risk factor compared to its absence. The odd's ratio is calculated as the ratio of the odds of disease in the exposed group (smokers) to the odds of disease in the non-exposed group (non-smokers).

**Why the Correct Answer is Right**
To calculate the odd's ratio, we use the following formula:

Odd's Ratio = (a / c) / (b / d)

where a = 30 (smokers with lung cancer), b = 10 (non-smokers with lung cancer), c = 20 (smokers without lung cancer), and d = 40 (non-smokers without lung cancer).

Plugging in the numbers, we get:

Odd's Ratio = (30 / 20) / (10 / 40)
Odd's Ratio = 1.5 / 0.25
Odd's Ratio = 6

This means that smokers are 6 times more likely to develop lung cancer than non-smokers.

**Why Each Wrong Option is Incorrect**

**Option A:**
This option is incorrect because the calculated odd's ratio is not 4. The actual calculation shows that the odd's ratio is 6, not 4.

**Option B:**
This option is incorrect because the calculated odd's ratio is not 2.8. The actual calculation shows that the odd's ratio is 6, not 2.8.

**Option D:**
This option is incorrect because the calculated odd's ratio is not 7. The actual calculation shows that the odd's ratio is 6, not 7.

**Clinical Pearl / High-Yield Fact**
Remember that the odd's ratio is a measure of association and not causation. It does not imply that smoking causes lung cancer, but rather that there is a strong association between the two.

**✓ Correct Answer: C. 6**