Out of all the patients in a hospital 89% are | vedclass

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Question

(A) Let $A$ be the set of patients with heart ailment and $B$ be the set of patients with lung infection. Given $n(A) = 89\%$ and $n(B) = 98\%$. We kn

Vedclass · Accepted Answer

$\{79, 81, 83, 85\}$

Vedclass · Answer

(A) Let $A$ be the set of patients with heart ailment and $B$ be the set of patients with lung infection. Given $n(A) = 89\%$ and $n(B) = 98\%$. We know that $n(A \cup B) = n(A) + n(B) - n(A \cap B)$. Since $n(A \cup B) \leq 100\%$,we have $89 + 98 - n(A \cap B) \leq 100$. $187 - n(A \cap B) \leq 100 \implies n(A \cap B) \geq 87$. Also,$n(A \cap B)$ cannot exceed the smaller of the two sets,so $n(A \cap B) \leq 89$. Thus,$87 \leq K \leq 89$. Therefore,$K$ must be in the range $[87, 89]$. Checking the options,the set $\{79, 81, 83, 85\}$ contains values that are not in the range $[87, 89]$.

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments,then $K$ cannot belong to the set :

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