How many students have got 60% or more marks in all the subjects?
Step 1: Let's assume the marks obtained by students in different subjects are provided as follows:
\[ \begin{aligned} &\text{Student 1: } 85, 60, 70, 80, 75, 90. \\ &\text{Student 2: } 95, 100, 90, 85, 88, 92. \\ &\text{Student 3: } 40, 50, 60, 70, 80, 90. \\ &\text{Student 4: } 60, 55, 65, 70, 60, 75. \end{aligned} \]Step 2: To check whether a student has 60% or more marks in all subjects, we need to see if the student’s marks in each subject are 60 or above.
Thus, only Student 1 and Student 2 qualify.
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 \( A_2 \)?