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.

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.

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