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Mathematics · 2024 · 4 marks
CBSE 2024 · Region 1 · Set 1 · Q37
According to recent research, air turbulence has increased in various regions around the world due to climate change. Turbulence makes flights bumpy…
According to recent research, air turbulence has increased in various regions around the world due to climate change. Turbulence makes flights bumpy and often delays the flights. Assume that, an airplane observes severe turbulence, moderate turbulence or light turbulence with equal probabilities. Further, the chance of an airplane reaching late to the destination are $\displaystyle 55 \%, 37 \%$ and $\displaystyle 17 \%$ due to severe, moderate and light turbulence respectively.
On the basis of the above information, answer the following questions :
(i)
Find the probability that an airplane reached its destination late.
(ii)
If the airplane reached its destination late, find the probability that it was due to moderate turbulence. Case Study - $\displaystyle 3$
Marking-scheme solution
(i)
Let A denote the event of airplane reaching its destination late
$\displaystyle E_{1}=$ severe turbulence
$\displaystyle E_{2}=$ moderate turbulence
$\displaystyle E_{3}=$ light turbulence
$\displaystyle \mathrm{P}(\mathrm{A})=\mathrm{P}\left(E_{1}\right) \mathrm{P}\left(\mathrm{A} \mid E_{1}\right)+\mathrm{P}\left(E_{2}\right) \mathrm{P}\left(\mathrm{A} \mid E_{2}\right)+\mathrm{P}\left(E_{3}\right) \mathrm{P}\left(\mathrm{A} \mid E_{3}\right)$
$\displaystyle =\frac{\mathbf{1}}{\mathbf{3}} \boldsymbol{\times} \frac{\mathbf{5 5}}{\mathbf{1 0 0}} \boldsymbol{+} \frac{\mathbf{1}}{\mathbf{3}} \boldsymbol{\times} \frac{\mathbf{3 7}}{\mathbf{1 0 0}} \boldsymbol{+} \frac{\mathbf{1}}{\mathbf{3}} \boldsymbol{\times} \frac{\mathbf{1 7}}{\mathbf{1 0 0}}$
$\displaystyle =\frac{\mathbf{1}}{\mathbf{3}}\left(\frac{\mathbf{1 0 9}}{\mathbf{1 0 0}}\right)=\frac{\mathbf{1 0 9}}{\mathbf{3 0 0}}$
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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.