List I Probability of an event | List II Value | ||
(A) | P(A∩Bc) | (I) | \(\frac{2}{3}\) |
(B) | P(A∪Bc) | (II) | \(\frac{1}{3}\) |
(C) | P(Ac∩Bc) | (III) | \(\frac{5}{6}\) |
(D) | P(Ac∪Bc) | (IV) | \(\frac{1}{6}\) |
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 \( A_2 \)?