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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 2 · Set 2 · Q36
Three persons viz. Amber, Bonzi and Comet are manufacturing cars which run on petrol and on battery as well. Their production share in the market is…
Three persons viz. Amber, Bonzi and Comet are manufacturing cars which run on petrol and on battery as well. Their production share in the market is $\displaystyle 60 \%, 30 \%$ and $\displaystyle 10 \%$ respectively. Of their respective production capacities, $\displaystyle 20 \%, 10 \%$ and $\displaystyle 5 \%$ cars respectively are electric (or battery operated) . Based on the above, answer the following:
(i)
(a)
What is the probability that a randomly selected car is an electric car?
OR
(b)
What is the probability that a randomly selected car is a petrol car?
(ii)
A car is selected at random and is found to be electric. What is the probability that it was manufactured by Comet?
(iii)
A car is selected at random and is found to be electric. What is the probability that it was manufactured by Amber or Bonzi?
Marking-scheme solution
\[\mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{E}}\right)=\frac{\mathrm{P}(\mathrm{C}) \times \mathrm{P}\left(\dfrac{\mathrm{E}}{\mathrm{C}}\right)}{\mathrm{P}(\mathrm{E})}
\]
$\displaystyle =\frac{\dfrac{10}{100} \times \dfrac{5}{100}}{\dfrac{60}{100} \times \dfrac{20}{100}+\dfrac{30}{100} \times \dfrac{10}{100}+\dfrac{10}{100} \times \dfrac{5}{100}}$
$\displaystyle =\frac{\dfrac{50}{10000}}{\dfrac{1550}{10000}}=\frac{1}{31}$
$\displaystyle \mathrm{P}\left(\frac{\mathrm{A} \text { or } \mathrm{B}}{\mathrm{E}}\right)=1-\mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{E}}\right)=1-\frac{1}{31}=\frac{30}{31}$
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CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.