In a study published in 2002, 450 patients who suffered fromcardiac arrest were

Question

In a study published in 2002, 450 patients who suffered fromcardiac arrest were sampled. Among the The Consumers Union led astudy for the Untied States Department of Agriculture on thepresence or absense of pesticide residues in foods. In the 19,514samples in which pesticide presence was determined, 29 wereorganically grown, while among the 7,184 samples in whichpesticides was not found, 98 were organically grown. Is thepresence or abscence of pesticide independent or whether the foodwas organically gornw? In a study published in 2002, 450 patients who suffered fromcardiac arrest were sampled. Among the The Consumers Union led astudy for the Untied States Department of Agriculture on thepresence or absense of pesticide residues in foods. In the 19,514samples in which pesticide presence was determined, 29 wereorganically grown, while among the 7,184 samples in whichpesticides was not found, 98 were organically grown. Is thepresence or abscence of pesticide independent or whether the foodwas organically gornw?

Explanation / Answer

   P( organically grown ) = (29+98) / (19514 + 7184) = 127 / 26698    P(absences of pesticide and organically grown ) = 98 /26698    P(presence of pesticide and organically grown ) = 29 /26698    Now, P( presence of pesticide) x P(organically grown ) =(19514 / 26698 ) x (127 / 26698 ) ˜0.0035 and P(presence of pesticide and organically grown ) =98 / 26698 ˜ 0.0037 which is very close to0.0035 therefore, we can conclude that the presence of pesticide isindependent of whether the food was organically grown. Similarly, P( absence of pesticide) x P(organically grown ) =(7184 / 26698 ) x (127 / 26698 ) ˜0.0013 and P(absence of pesticide and organically grown ) =29 / 26698 ˜ 0.0011 which is very close to 0.0013 therefore, we can conclude that the absence of pesticide isalso independent of whether the food was organicallygrown.

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