List-I (Sentences) | List-II (Adverbs) |
(A) \( P(A \cap B) \) | (I) \(\frac{2}{5}\) |
(B) \( P(A | B) \) | (II)\( \frac{4}{15}\) |
(C) \( P(A' | B) \) | (III) \(\frac{3}{5}\) |
(D) \( P(A' \cap B') \) | (IV) \(\frac{2}{9}\) |
Based upon the results of regular medical check-ups in a hospital, it was found that out of 1000 people, 700 were very healthy, 200 maintained average health and 100 had a poor health record.
Let \( A_1 \): People with good health,
\( A_2 \): People with average health,
and \( A_3 \): People with poor health.
During a pandemic, the data expressed that the chances of people contracting the disease from category \( A_1, A_2 \) and \( A_3 \) are 25%, 35% and 50%, respectively.
Based upon the above information, answer the following questions:
(i) A person was tested randomly. What is the probability that he/she has contracted the disease?}
(ii) Given that the person has not contracted the disease, what is the probability that the person is from category \( A_2 \)?