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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 3 · Set 1 · Q31
A survey was conducted on the patients who have undergone knee replacement surgeries. It was found that, Robotic Knee replacement surgeries have 90%…
A survey was conducted on the patients who have undergone knee replacement surgeries.
It was found that, Robotic Knee replacement surgeries have $\displaystyle 90$% 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.
Marking-scheme solution
$\displaystyle P(\text{success})=\dfrac{9}{10}$ and $\displaystyle P(\text{not success})=\dfrac{1}{10}$
(i)
Probability that exactly one surgery is successful
$\displaystyle =\dfrac{9}{10} \times \dfrac{1}{10} \times \dfrac{1}{10} \times 3=\dfrac{27}{1000}$
(ii)
Probability that all three surgeries are successful
$\displaystyle =\dfrac{9}{10} \times \dfrac{9}{10} \times \dfrac{9}{10}=\dfrac{729}{1000}$
Probability that at most two surgeries are successful
$\displaystyle =1-\dfrac{729}{1000}=\dfrac{271}{1000}$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.