If p denotes proportion and q denotes odds then prove that

Question

If p denotes proportion and q denotes odds then prove that Find the range of q. If the odds of smokers in a study are 0.75 then find the proportion of smokers in the study. Assume that each subject of the study is either a smoker or a non-smoker.

18 Apr 2025

Answer :

Word Count : 469

In epidemiology and clinical trials, it is important to understand the relationship between proportion and odds, as they are often used to describe the likelihood of an event or condition occurring in a population. The goal here is to prove the range of odds qq in terms of the proportion pp, and to use this relationship to determine the proportion of smokers in a study, given the odds of smoking.

Let pp denote the proportion of subjects in a study who have a certain characteristic, in this case, being smokers. The proportion pp is defined as:

p=number of smokerstotal number of subjectsp = \frac{\text{number of smokers}}{\text{total number of subjects}}

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