CBSE 2025 · Region 1 · Set 1 · Q38 · 4 marks
A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate or variable rate with probabilities $\displaystyle 10 \%, 20 \%$ and $\displaystyle 70 \%$ respectively. A customer after availing loan can pay the loan or default on loan repayment. The bank data suggests that the probability that a person defaults on loan after availing it at fixed rate, floating rate and variable rate is $\displaystyle 5 \%, 3 \%$ and $\displaystyle 1 \%$ respectively. Based on the above information, answer the following:(i)What is the probability that a customer after availing the loan will default on the loan repayment?(ii)A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest?
A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate or variable rate with probabilities $\displaystyle 10 \%, 20 \%$ and $\displaystyle 70 \%$ respectively. A customer after availing loan can pay the loan or default on loan repayment. The bank data suggests that the probability that a person defaults on loan after availing it at fixed rate, floating rate and variable rate is $\displaystyle 5 \%, 3 \%$ and $\displaystyle 1 \%$ respectively. Based on the above information, answer the following:
(i)
What is the probability that a customer after availing the loan will default on the loan repayment?
(ii)
A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest?
Marking-scheme solution
\(\displaystyle E_{1}\) :customer avails loan on fixed rate \(\displaystyle \boldsymbol{E}_{\mathbf{2}}\) :customer avails loan on floating rate \(\displaystyle \boldsymbol{E}_{3}\) :customer avails loan on variable rate A:the person defaults on the loan
\[\begin{aligned}
& \mathrm{P}\left(E_{1}\right)=\frac{1}{10}, \mathrm{P}\left(E_{2}\right)=\frac{2}{10}, \mathrm{P}\left(E_{3}\right)=\frac{7}{10} \\
& \mathrm{P}\left(A \mid E_{1}\right)=\frac{5}{100}, \mathrm{P}\left(A \mid E_{2}\right)=\frac{3}{100}, \mathrm{P}\left(A \mid E_{3}\right)=\frac{1}{100}
\end{aligned}
\]
ProbabilityBayes' TheoremApplycase_studymedium
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CBSE Class 12 Mathematics past-paper question from the 2025board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.