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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 2 · Set 3 · Q36
Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality…
Airplanes are by far the safest mode of transportation when the number of transported passengers are measured against personal injuries and fatality totals.
Previous records state that the probability of an airplane crash is $\displaystyle 0 \cdot 00001 \%$. Further, there are $\displaystyle 95 \%$ chances that there will be survivors after a plane crash. Assume that in case of no crash, all travellers survive. Let $\displaystyle \mathrm{E}_{1}$ be the event that there is a plane crash and $\displaystyle \mathrm{E}_{2}$ be the event that there is no crash. Let A be the event that passengers survive after the journey. On the basis of the above information, answer the following questions :
(i)
Find the probability that the airplane will not crash.
(ii)
$$ Find $\displaystyle \mathrm{P}\left(\mathrm{A} \mid \mathrm{E}_{1}\right)+\mathrm{P}\left(\mathrm{A} \mid \mathrm{E}_{2}\right)$.
(iii)
(a)
Find $\displaystyle \mathrm{P}(\mathrm{A})$.
OR
(b)
Find $\displaystyle \mathrm{P}\left(\mathrm{E}_{2} \mid \mathrm{A}\right)$. Case Study - $\displaystyle 2$
Marking-scheme solution
(i)
$\displaystyle \mathrm{P}\left(\mathrm{E}_{2}\right)=1-0.0000001$
$\displaystyle =0.9999999$
(ii)
$\displaystyle \mathrm{P}\left(\mathrm{A} / \mathrm{E}_{1}\right)+\mathrm{P}\left(\mathrm{A} / \mathrm{E}_{2}\right)=\frac{95}{100}+1=\frac{195}{100}$
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CBSE Class 12 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.