It is given that,
Total students = 100
Girls = 25, Boys = 75
Rich = 20
Poor = 80
Fair complexion = 40, Dark = 60
Probability of selecting:
a girl = \(\frac{25}{100}\)
= \(\frac{1}{4}\)
a rich person = \(\frac{20}{100}\)
= \(\frac{1}{5}\)
a fair person = \(\frac{40}{100}\)
= \(\frac{2}{5}\)
Therefore, Probability of selecting a fair complexioned rich girl is
= \(\frac{1}{4}\times1\times5\times\frac{2}{5}\)
= \(0.02\)
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 \( A_2 \)?