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Game Theory · Information cascades & Bayes' rule

12 questions · 17 marks · 3 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Game Theory and Strategy

Information cascades & Bayes' rule

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

End Term · 31 Aug 2025 (FN)End Term

Read the passage below, then answer Q1–Q2
Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.
Q1NAT2 Marks·Write the number
Asked 3 times Key ↓
If an item is selected at random, the probability that the item is defective is _____________
Your answer:
Q2NAT2 Marks·Write the number
Asked 4 times Key ↓
Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ______________
Your answer:
Q3MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Consider following two statements: 1. Crowd can be wrong even if everyone in the crowd is rational and everyone takes the same action. 2. Aggregate behaviour of many people with limited information can sometimes produce very accurate results. Which statement(s) is (are) true?
1. AOnly 1
2. BOnly 2
3. CBoth 1 & 2
4. DNone

End Term · 31 Aug 2025 (AN)End Term

Read the passage below, then answer Q4–Q5
Three machines, A, B, and C, produce respectively 50%, 30% and 20% of the total no. of items of a factory. The percentages of defective output of these machines are 3%, 4% and 5%.
Based on the above data, answer the given subquestions.
Q4NAT2 Marks·Write the number
Asked 3 times Key ↓
If an item is selected at random, the probability that the item is defective is ______________
Your answer:
Q5NAT2 Marks·Write the number
Asked 4 times Key ↓
Suppose an item is selected at random and found to be defective. The probability that the item was produced by machine A will be ____________
Your answer:
Q6MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Consider following two statements: 1. Crowd can be never be wrong even if everyone in the crowd is rational and everyone takes the same action. 2. Aggregate behaviour of many people with limited information can never produce very accurate results. Which statement(s) is (are) true?
1. AOnly 1
2. BOnly 2
3. CBoth the Only 1 & Only 2
4. DNone

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Read the passage below, then answer Q7–Q12
Consider the example of cascade discussed in the lecture but with a modification that now the urn is containing either 4 blue balls and 2 red ball or 4 red balls and 2 blue ball with equal probability. That simply means that the urn is equally likely to be blue-majority urn or red-majority urn. We assume everyone hears what the previous individuals report and get their own private signal by randomly drawing one ball from the urn.
Based on the above data, answer the given subquestions.
Q7MCQ1 Mark·Choose one option
Key ↓
Suppose one ball is picked from the red majority urn. What is the probability that the ball is blue?
1. A1/3
2. B3/4
3. C1/4
4. D2/3
Q8MCQ1 Mark·Choose one option
Asked 4 times Key ↓
What is the probability that the urn is majority-red if the first student draws a blue ball?
1. A1/5
2. B4/5
3. C2/3
4. D1/3
Q9MCQ1 Mark·Choose one option
Key ↓
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red). What is the probability of getting this sequence if the urn is a blue-majority urn?
1. A5/27
2. B4/27
3. C16/125
4. D9/125
Q10MCQ1 Mark·Choose one option
Key ↓
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red). What is the probability of getting this sequence if the urn is a red-majority urn?
1. A2/27
2. B5/27
3. C5/216
4. D7/216
Q11MCQ1 Mark·Choose one option
Asked 3 times Key ↓
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red). What is the total probability of getting this sequence?
1. A1/25
2. B2/25
3. C1/9
4. D2/9
Q12MCQ2 Marks·Choose one option
Asked 4 times Key ↓
Now suppose, first three students draw the ball in the sequence (Blue, Blue, Red). What is the probability of urn being red-majority in this scenario?
1. A2/3
2. B1/25
3. C4/25
4. D1/3

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q10.035 to 0.04

Q20.4 to 0.405

Q3C

Q40.035 to 0.04

Q50.4 to 0.405

Q6D

Q7A

Q8D

Q9B

Q10A

Q11C

Q12D

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.