Read the Passage
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 10%, 20% and 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 5%, 3% and 1% respectively.
COMPETENCY BASED
APPLY
2 Marks
2025
AISSCE(Board Exam)
VSA
What is the probability that a customer after availing the loan will default on the loan repayment?
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Step-by-Step Solution
Let F, G, and V denote the events that a customer avails loan on fixed rate, floating rate, and variable rate, respectively. Let D denote the event that a customer defaults on the loan repayment.
We are given the following probabilities:
- P(F) = 0.10
- P(G) = 0.20
- P(V) = 0.70
- P(D|F) = 0.05
- P(D|G) = 0.03
- P(D|V) = 0.01
We want to find the probability that a customer will default on the loan repayment, which is P(D). We can use the law of total probability to find P(D):
P(D) = P(D|F)P(F) + P(D|G)P(G) + P(D|V)P(V)
P(D) = (0.05)(0.10) + (0.03)(0.20) + (0.01)(0.70)
P(D) = 0.005 + 0.006 + 0.007
P(D) = 0.018
Correct Answer: 0.018
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Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because the student needs to apply the concepts of probability and conditional probability to solve a real-world problem.
Knowledge Dimension:
CONCEPTUAL
Justification:
The question requires understanding of probability concepts like conditional probability and the law of total probability to arrive at the solution.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as COMPETENCY. The question is designed to assess the student's ability to apply probability concepts to a real-world scenario, aligning with competency-based education principles.
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