Appeared in: 2026 (2 sets)
A survey was conducted on the patients who have undergone knee replacement surgeries.
It was found that, Robotic Knee replacement surgeries have $90%$ success rate.
On a particular day, robotic surgery was performed on three patients, A, B and C, one after the other. Assuming that the success and failure of each surgery is independent of each other, find the probability that :
(i) exactly one surgery is successful,
(ii) at most two surgeries are successful.