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A study of 380 diabetics and non diabetics classified as underweight, normal weight and obese ....

A study of 380 diabetics and non diabetics classified as underweight, normal weight and obese . Probability of normal weight 0.31. Probability of having diabetes is 0.39. The probability of being normal weight and diabetic is 0.09. Comparing the unconditional probability of having diabetes to the conditional probability of diabetes given weight would you say weight and diabetes are independent?

Math   Statistics-And-Probability   
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Answer #1

Given

P(normal weight) = 0.31

P(diabetes) = 0.39

P(normal weight and diabetes ) = P( normal weight diabetes) = 0.09

So, P(diabetes | normal weight ) = P( normal weight diabetes) / P(normal weight)

Now,

P(diabetes | normal weight ) P(diabetes)

So, we can say weight and diabetes are not independent

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