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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 4 · Set 1 · Q37
A building contractor undertakes a job to construct 4 flats on a plot along with parking area. Due to strike the probability of many construction…
A building contractor undertakes a job to construct $\displaystyle 4$ flats on a plot along with parking area. Due to strike the probability of many construction workers not being present for the job is $\displaystyle 0 \cdot 65$. The probability that many are not present and still the work gets completed on time is $\displaystyle 0.35$ . The probability that work will be completed on time when all workers are present is $\displaystyle 0 \cdot 80$. Let: $\displaystyle \mathrm{E}_{1}$ : represent the event when many workers were not present for the job; $\displaystyle \mathrm{E}_{2}$ : represent the event when all workers were present; and E : represent completing the construction work on time. Based on the above information, answer the following questions :
(i)
What is the probability that all the workers are present for the job?
(ii)
What is the probability that construction will be completed on time?
(iii)
(a)
What is the probability that many workers are not present given that the construction work is completed on time?
OR
(b)
What is the probability that all workers were present given that the construction job was completed on time? Case Study - $\displaystyle 3$
Marking-scheme solution
(i)
$\displaystyle \mathrm{P}\left(\mathrm{E}_{2}\right)=1-\mathrm{P}\left(\mathrm{E}_{1}\right)=1-0 \cdot 65=0 \cdot 35$
(ii)
$\displaystyle \mathrm{P}(\mathrm{E})=\mathrm{P}\left(\mathrm{E}_{1}\right) \cdot \mathrm{P}\left(\frac{\mathrm{E}}{\mathrm{E}_{1}}\right)+\mathrm{P}\left(\mathrm{E}_{2}\right) \cdot \mathrm{P}\left(\frac{\mathrm{E}}{\mathrm{E}_{2}}\right)$
$$=$\displaystyle 0$ \cdot $\displaystyle 65$ \times $\displaystyle 0$ \cdot $\displaystyle 35$+$\displaystyle 0$ \cdot $\displaystyle 35$ \times $\displaystyle 0$ \cdot $\displaystyle 8$
$$$$
=$\displaystyle 0$ \cdot $\displaystyle 51$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.