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Basic Math/How to combine two percentage (which may have overlap)

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Question
Hello,

I am doing a research and lets say i have a 100 patients , 50% who have a certain heart disease , and 60% who have another heart disease. There might be some overlap between those two (some patients may have both heart diseases but i have no information on their percentage)

Is there any way i can combine those two percentages to find a percentage of patients who have a heart disease (whether they have heart disease A or heart disease B or both)

Thank you very much,
Ahmad

Answer
Hello Ahmad,

In this case we can use the well-known formula in probability: P(A or B) = P(A) + P(B) - P(A and B)

However, we only know P(A)=0.5 and P(B)=0.6, we need one more piece of info...either P(A and B)
to determine P(A or B), or P(A or B) to determine P(A and B).

All we can say now, with limited info, is that since P(A) + P(B) = 1.1, which is greater than
100%, is that P(A and B) must be AT LEAST 0.1 or 10%, since P(A or B) cannot exceed 100%.

I hope this helps.

A. Mantell

Basic Math

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations belong to
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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