Indian Institute of Technology Madras
BS Degree Programme · Examination & Study Paper
Business Analytics
Probability, Bayes & distributions
Examination Instructions & Guidelines
- Solve on notebook/paper first before checking solutions.
- MCQ: Exactly 1 option is correct. Negative marking applies.
- MSQ: One or more options correct. Select all to score.
- NAT: Numerical response. No negative marking.
- Scientific calculator allowed for all calculations.
- Official answer key is sealed at the end of this sheet.
Quiz 1 · 26 Oct 2025 (AN)Quiz 1
- Q1MSQ1 Mark·Choose all correct options
Which of the following distributions is/are Symmetric in nature (choose all that are applicable)?
- AStandard Normal distribution
- BStandard Binomial distribution
- CUniform distribution
- DPoisson distribution
Read the passage below, then answer Q2–Q4
(The following is a purely imaginary scenario)
An insurance company believes that people can be divided into two classes: “Class-1: Those who are accident prone” and “Class-2: Those who are not accident prone”. The company’s statistics show that an accident-prone person will have an accident at sometime within a fixed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. It is assumed that 30 percent of the human population is accident prone. Given this information, answer the sub-questions.
Q2NAT1 Mark·Write the numberWhat is the probability that a new policyholder will have an accident within a year of purchasing a policy? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer:- Q3NAT1 Mark·Write the number
Suppose you learn that a new policyholder has an accident within a year of purchasing a policy. Then, what is the probability that the person is accident prone? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.235”, then enter it as “1.24”)
Your answer: - Q4NAT1 Mark·Write the number
The insurance company has to pay an insurance fee of Rs. 10 per accident if the accident happens in the first year. If the company has sold 1000 insurances in total, then how much money (in Rs.) will it expect to pay at the end of the first year for Class-2 people? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “Rs. 1.235”, then enter it as “1.24”)
Your answer:
End Term · 31 Aug 2025 (FN)End Term
- Q5MCQ1.5 Marks·Choose one option
The Following Question is Purely Hypothetical Your family is seeking an alliance for you and has found three matrimonial services “X”, “Y” and “Z”. Assume that the enrolment in the matrimonial services is mutually exclusive. A market survey indicates that 40% of total enrolments are in “X”, 35% are in “Y” and the remaining are in “Z”. The market survey also indicates that 25% of registrations in “X” find a suitable match, 40% in “Y” find a suitable match, and 30% in “Z” find a suitable match. Recently, your family has heard the news that a relative “P” has not found a suitable match after enrolling in one of the matrimonial services. Then which matrimonial service would you suspect “P” to have enrolled in?
- AZ
- BY
- CX
- DCannot say as I am already married (This is not the correct answer to this question. Just relax, think and choose from the other three)
End Term · 13 Apr 2025 (FN)End Term
- Q6MSQ1 Mark·Choose all correct options
Which of the following distributions is/are not symmetric in nature (choose all that are applicable)?
- AStandard Normal distribution
- BStandard Binomial distribution
- CUniform distribution
- DPoisson distribution
- Q7MSQ1 Mark·Choose all correct options
Which of the following is/are required to build an empirical distribution? (choose all that are applicable)
- APDF or PMF
- BSample data
- CSummary Statistics
- DNone of these
Read the passage below, then answer Q8–Q9
(The following is a purely imaginary scenario)
An insurance company believes that people can be divided into two classes: “Class-1: Those who are accident prone” and “Class-2: Those who are not accident prone”. The company’s statistics show that an accident-prone person will have an accident at sometime within a faxed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone. It is assumed that 30 percent of the human population is accident prone. Given this information, answer the sub-questions
Q8NAT1 Mark·Write the numberWhat is the probability that a new policyholder will have an accident within a year of purchasing a policy? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:- Q9NAT1 Mark·Write the number
Suppose a new policyholder has an accident within a year of purchasing a policy. Then, what is the probability that the person is accident prone? (Note: Enter the answer rounded to two decimal places. For example, if the answer is “1.234”, then enter it as “1.23”)
Your answer:
End Term · 22 Dec 2024 (AN)End Term
- Q10NAT2 Marks·Write the number
Two factories “A” and “B” produce radios. Each radio produced at factory-A is defective with probability 0.05, whereas each radio produced at factory-B is defective with probability 0.1. You purchase two radios that were produced in the same factory (which is equally likely to have been either factory-A or factory-B). If the first radio that you check is defective, what is the conditional probability that the second radio is also defective? (Note: Enter your answer in decimals rounded to two decimal places. For example, if your answer is “0.456” then enter it as “0.46”)
Your answer: