The probability of an event lies between 0 and 1, inclusive. This means: \[ 0 \leq P(\text{Event}) \leq 1 \] Option (A) 0 is a valid probability, representing an impossible event.
Option (B) 1 is a valid probability, representing a certain event.
Option (D) 0.99999 is a valid probability, as it is still within the range [0, 1].
However, option (C) 1.0001 is not a valid probability because it exceeds the upper limit of 1.
The correct option is (C): \(1·0001\)
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 \( A_2 \)?