CBSE 2026 · Region 3 · Set 1 · Q37 · 4 marks
A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII.
As per the data collected, $\displaystyle 40$% students appearing in the examination were dropouts and the remaining students were regular students of class XII. Of the dropouts, $\displaystyle 5$% qualify the examination while $\displaystyle 10$% of the regular students qualify the examination. Based on the above information, answer the following questions.(i)Find the probability that a student selected at random is a regular student.(ii)A student is selected at random from a group of dropout students. What is the probability that the student will not qualify the examination ?(iii)A student selected at random qualified the examination. Find the probability that student is not a dropout.A student selected at random did not qualify the examination. Find the probability that the student was a regular student.
A survey was conducted to find out the success rate of students who qualified the entrance examination by dropping a year after class XII.
As per the data collected, $\displaystyle 40$% students appearing in the examination were dropouts and the remaining students were regular students of class XII. Of the dropouts, $\displaystyle 5$% qualify the examination while $\displaystyle 10$% of the regular students qualify the examination. Based on the above information, answer the following questions.
(i)
Find the probability that a student selected at random is a regular student.
(ii)
A student is selected at random from a group of dropout students. What is the probability that the student will not qualify the examination ?
(iii)
A student selected at random qualified the examination. Find the probability that student is not a dropout.
A student selected at random did not qualify the examination. Find the probability that the student was a regular student.
Marking-scheme solution
(i)
Probability that a student selected at random is a regular student $\displaystyle =\dfrac{3}{5}$
(ii)
Probability that the selected student from the group of dropout will not qualify the examination $\displaystyle =\dfrac{95}{100}$ or $\displaystyle \dfrac{19}{20}$
(iii)
Let A : The student has qualified the examination.
$\displaystyle E_{1}$ : The student appearing in the examination is dropout.
$\displaystyle E_{2}$ : The student is regular.
Using Bayes' Theorem, $\displaystyle P\left(\dfrac{E_{1}{}^{\prime}}{A}\right)=P\left(\dfrac{E_{2}}{A}\right)=\dfrac{\frac{60}{100} \times \frac{10}{100}}{\frac{40}{100} \times \frac{5}{100}+\frac{60}{100} \times \frac{10}{100}}$
$\displaystyle =\dfrac{3}{4}$
$\displaystyle P\left(\dfrac{E_{2}}{A^{\prime}}\right)=\dfrac{\frac{60}{100} \times \frac{90}{100}}{\frac{40}{100} \times \frac{95}{100}+\frac{60}{100} \times \frac{90}{100}}$
$\displaystyle =\dfrac{27}{46}$
ProbabilityBayes' TheoremApplycase_studymedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.