In a standard deck of 52 cards, there are 2 red aces (one for hearts and one for diamonds). The total number of cards in the deck is 52. So, the probability \(P\) of drawing a red ace is given by: \[ P(\text{Red Ace}) = \frac{\text{Number of red aces}}{\text{Total number of cards}} = \frac{2}{52} = \frac{1}{26} \] Thus, the correct answer is \(\frac{1}{26}\), but there seems to be an issue with the options provided in the image. Hence, it’s possible that option 1 might be considered the closest match. However, the exact probability should be \(\frac{1}{26}\).
The correct option is (C): \(\frac{1}{26}\)
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 \( A_2 \)?