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Old 05-23-2015
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Default Biostatistics question

Hello all

Question about biostats from Kaplan: chance of meeting someone who is obese, has diabetes, or both? probability that obese = 30%, probability that diabetic = 10%

So my question is, why don't we add up these probabilities: {someone who is obese} + {probability of someone who is diabetic} + {someone who is both}?

In the solutions, they just found the probability the following way:
(10 + 30) - (10*30).
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Old 05-23-2015
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Chances that they have both = .1 x .3
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Old 05-23-2015
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Default Explanation

Obese = 30%
Diabetes = 10%


Probability of having BOTH: 30% x 10% = 3%
Probability of having NEITHER: (100%-30%) x (100%-10%) = 63%
Probability of having Obesity ONLY = 30% - Probability of having both obesity and DM = 30% - 3% = 27%
Probability of having Diabetes ONLY = 10% - Probability of having obesity and DM = 10% - 3% = 7%

This is every situation. Let's see if it adds up: 3 + 63 + 27 + 7 = 100%. Success!
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Old 05-23-2015
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Quote:
Originally Posted by giraffeegiraffee View Post
Obese = 30%
Diabetes = 10%


Probability of having BOTH: 30% x 10% = 3%
Probability of having NEITHER: (100%-30%) x (100%-10%) = 63%
Probability of having Obesity ONLY = 30% - Probability of having both obesity and DM = 30% - 3% = 27%
Probability of having Diabetes ONLY = 10% - Probability of having obesity and DM = 10% - 3% = 7%

This is every situation. Let's see if it adds up: 3 + 63 + 27 + 7 = 100%. Success!
Thank you for your response. Unless I am misreading the question, I think they want us to calculate the TOTAL probability of meeting EITHER an obese person, OR a diabetic, OR both. So what I think is we should add it up as probability of meeting someone who is obese (ie 30) + probability of meeting a diabetic (ie 10) + probability of meeting someone who is both (ie [(10+30) - (10*30)]:

10+ 30 + [ (10+30) - (10*30)]
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Old 05-24-2015
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Quote:
Originally Posted by ayeshak View Post
Thank you for your response. Unless I am misreading the question, I think they want us to calculate the TOTAL probability of meeting EITHER an obese person, OR a diabetic, OR both. So what I think is we should add it up as probability of meeting someone who is obese (ie 30) + probability of meeting a diabetic (ie 10) + probability of meeting someone who is both (ie [(10+30) - (10*30)]:

10+ 30 + [ (10+30) - (10*30)]
Since diabetes and obesity are not mutually exclusive you can not just add them together. Being obese does not mean that you can not be diabetic and the same is true the other way around, being diabetic does not mean that you can not be obese. When they say that probability of meeting somebody who is obese is 30%, that 30% includes all the obese diabetics in it. What 30% says is that 30 out of 100 people are obese but it does NOT say that those 30 people are ONLY obese, some of those 30 might be diabetic, some of them might have heart disease, some of them might be smokers, who knows. Prevalence of diabetes is 10%, so 10 out of a 100 are going to be diabetic, however, again, a portion of those 10 diabetics are going to be obese.

If you add those two percentages together you will be summing up (1) people with diabetes who are NOT obese + (2) people with diabetes who are obese + (3) people who are obese and do NOT have diabetes + (4) people who are obese and have diabetes. If you look closely, number 2 and number 4 are the exact same thing. So in a straightforward addition of two rates you include obese diabetics TWICE. So you need to subtract the probability of meeting a person who is BOTH obese and diabetic from that formula. Chance of meeting a person who is both obese and diabetic is 0.1x0.3. Why? Because the probability of meeting somebody who is obese is 30% and of those 30%, 10% are going to be diabetic (because that is the prevalence of diabetes). What is 10% of 30%? 3%. (This formula does not take into account that obese people have a higher prevalence of having diabetes as compared to general population).

Finally you get 10%+30%-3%=37%
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