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#1




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). 
#2




Chances that they have both = .1 x .3

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#3




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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#4




Quote:
10+ 30 + [ (10+30)  (10*30)] 
#5




Quote:
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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