LIST I | LIST II | ||
A. | Addition Theorem on probability | I. | \(P(Ei/A)=\frac{p(Ei)P(A/Ei)}{\displaystyle\sum_{l=1}^nP(Ei)P(A/Ei)},i=1,2\) |
B. | Binomial distribution | II. | \(P(A\cap B)=P(A)P(B/A),if P(A)\neq0\) |
C. | Baye's rule | III. | \(P(A\cup B)=P(A)+P(A)+P(B)-P(A\cap B)\) |
D. | Multiplication theorem on prob | IV. | \(P(x=r)=^nC_rp^rq^{n-r},r=0,1,.....,n\) |
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 \( A_2 \)?