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Question

In a hospital, 89% has the disease A and 98% has the disease B, K% is the number of patients who has both, then K can't be the subset of


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Solution

Determine the minimum and maximum value of K

Let us assume that the total number of patients in the hospital is nT=100.

It is given that 89% has the disease A, 98% has the disease B and K% is the number of patients who has both.

Thus, the number of patients who have the disease A, nA=89.

The number of patients who have the disease B, nB=98.

The number of patients who have both the disease A and the disease B, nAB=K.

Hence, maxnA,nB=nB=98.

It is known that maxnA,nBnABnT.

98nAB100.

It is also known that nAB=nA+nB-nAB.

So, 98nA+nB-nAB100.

9889+98-nAB10098187-nAB10098-187-nAB100-187-89-nAB-8789nAB87

Thus, nAB87,89.

Hence, nAB is not a subset of x:x-87,89.


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