Question

25) The table below describes the smoking habits of a group of asthma sufferers.Light HeavyNonsmoker smoker smoker TotalMen390 34 42 466Women446 35 44525Total 836 69 86991If two different people are randomly selected from the 991 subjects, find the probability that they are bothheavy smokers. Round to six decimal places.

Answer 1

`Pr(\text{2 heavy smokers) = }0.007531`Step-by-step explanation:
`\begin{gathered} \text{Total smokers from the table = 991} \\ \text{Total }nu\text{mber of heavy smokers = 86} \\ \\ \text{probability of picking two heavy smokers = Pr(heavy smoker and heavy smoker)} \end{gathered}`
`Pr(\text{heavy smoker) = }\frac{Total\text{ }number\text{ of heavy smoker}}{\text{total smokers}}`
`\begin{gathered} Pr(\text{heavy smoker) = }(86)/(991) \\ \\ Pr(\text{2 heavy smokers) = }Pr(\text{heavy smoker) }*\text{ }Pr(\text{heavy smoker)} \end{gathered}`
`\begin{gathered} Pr(\text{2 heavy smokers) = }(86)/(991)*(86)/(991) \\ Pr(\text{2 heavy smokers) =}(7396)/(982081) \\ Pr(\text{2 heavy smokers) = }0.007531\text{ (6 decimal place)} \end{gathered}`