Step 1: Understand equally likely outcomes
Equally likely outcomes refer to situations where each possible outcome has the same probability of occurring.
Step 2: Analyze each option
Option (1): Tossing a coin has two equally likely outcomes: heads and tails.
Option (2): Tossing two coins simultaneously has four equally likely outcomes: (HH, HT, TH, TT).
Option (3): Rolling two dice also has 36 equally likely outcomes, as each die has 6 faces, giving 6 × 6 = 36 possibilities.
Step 3: Conclusion
All of the options represent situations with equally likely outcomes. Hence, the correct option is \( (4) \).
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 \( A_2 \)?