✓ Board-verified
Mathematics · 2025 · 4 marks
CBSE 2025 · Region 1 · Set 1 · Q38
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…
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
\[\begin{aligned}
& \mathrm{P}\left(E_{1}\right)=\frac{1}{10}, \mathrm{P}\left(E_{2}\right)=\frac{2}{10}, \mathrm{P}\left(E_{3}\right)=\frac{7}{10} \\
& \mathrm{P}\left(A \mid E_{1}\right)=\frac{5}{100}, \mathrm{P}\left(A \mid E_{2}\right)=\frac{3}{100}, \mathrm{P}\left(A \mid E_{3}\right)=\frac{1}{100}
\end{aligned}
\]
More from Probability
- Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is 1/3. Reason…2023
- If A and B are two events such that P(B)=1/5, P(A ∣ B)=2/3 and P(A ∪ B)=3/5, then P(A) is:2025
- A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances of their manufacturing a defective…2025
- Three friends A, B and C got their photograph clicked. Find the probability that B is standing at the central position, given that A is standing at…2022
- A box has 4 green, 8 blue and 3 red pens. A student picks up a pen at random, checks its colour and replaces it in the box. He repeats this process 3…2025
- Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000…2026
- Let M and N be two events such that P(M)=0.6, P(N)=0.2 and P(M ∩ N)=0.5, then P(M^′ / N^′) is2025
- The probability distribution of a random variable X is: where k is some unknown constant. The probability that the random variable X takes the value…2024
CBSE Class 12 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.