Step 1: Understand the relationship for complementary events
The probability of the complement of an event \( E \) is given by: \[ P(\text{not } E) = 1 - P(E) \] This represents the probability that event \( E \) does not occur.
Step 2: Identify the correct option
The correct formula for the probability of the complement of event \( E \) is \( 1 - P(E) \).
Step 3: Conclusion
Therefore, the correct option is \( (1) \).
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 \( A_2 \)?