In a study about a pandemic, data of 900 persons was collected. It...

We denote the set of people having symptoms of fever, cough and breathing problem by $F, C$ and $B$ respectively

Given that $n\left(F\right) = 190, n\left(B\right) = 220$ and $n\left(C\right) = 220$

Also given, $n\left(F \cup C\right) = 330, n\left(B \cup C\right) = 350,$ $n\left(F \cup B\right) = 340$ and $n\left(F \cap C \cap B\right) = 30$

So $n\left(F \cap C\right) = n\left(F\right) + n\left(C\right) - n\left(F \cup C\right)$

$= 80$

Similarly, $n\left(F \cap B\right) = n\left(F\right) + n\left(B\right) - n\left(F \cup B\right) = 70$ and $n\left(C \cap B\right) = n\left(C\right) + n\left(B\right) - n\left(B \cup C\right) = 90$

Putting the data in Venn diagram

Number of people having at most one symptom=Number of people having zero symptom or one symptom

$= 70 + 80 + 90 + 480 = 720$

Required probability $= \dfrac{720}{900} = 0 . 8$