Bag1 = 3 back, 4 white balls
Bag2 = 4 black, 3 white balls
Probability of selecting bag 1 \(=\frac{2}{6}=\frac{1}{3}\)
Probability of selecting bag 2 \(=1-\frac{1}{3}=\frac{2}{3}\)
Probability of choosing a black ball from bag 1 \(=\frac{3}{7}\)
Probability of choosing a black ball from bag 2 \(=\frac{4}{7}\)
Required probability \(=\frac{1}{3}\times\frac{3}{7}+\frac{2}{3}\times\frac{4}{7}\)
\(=\frac{11}{21}\).So the correct option is (A)
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 \( A_2 \)?