JEE Advanced 2022 Paper 1 · Q03 · Probability

Question

In a study about a pandemic, data of 900 persons was collected. It was found that 190 persons had symptom of fever, 220 persons had symptom of cough, 220 persons had symptom of breathing problem, 330 persons had symptom of fever or cough or both, 350 persons had symptom of cough or breathing problem or both, 340 persons had symptom of fever or breathing problem or both, 30 persons had all three symptoms (fever, cough and breathing problem). If a person is chosen randomly from these 900 persons, then the probability that the person has at most one symptom is _____________.

SolveKar AI · Accepted Answer

Let $F,C,B$ be the three sets. $|F\cup C|=|F|+|C|-|F\cap C|\Rightarrow |F\cap C|=190+220-330=80$. Similarly $|C\cap B|=220+220-350=90$ and $|F\cap B|=190+220-340=70$. Given $|F\cap C\cap B|=30$. Number with exactly two symptoms $=(|F\cap C|+|C\cap B|+|F\cap B|)-3|F\cap C\cap B|=80+90+70-90=150$. Number with all three $=30$. Persons with at least two symptoms $=150+30=180$. Persons with at most one symptom $=900-180=720$. Probability $=720/900=0.8$.

JEE Advanced 2022 Paper 1 · Q03 · Probability

Solution