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Stats I · Probability and conditional probability

BSMA1002 · 19 questions · 51 marks · 7 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1002 · Statistics for Data Science I

Probability and conditional probability

Official Paper

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.

End Term · 31 Aug 2025 (FN)End Term

Q1NAT3 Marks·Write the number
Key ↓
If two fair dice are thrown, what is the probability that the sum is either 4 or 9? Enter the answer correct to two decimal places.
Your answer:
Q2NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q3NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q4–Q5
A box contains 4 red balls and 5 blue balls. Three balls are drawn at random without replacement. Based on the above data, answer the given subquestions.
Q4NAT3 Marks·Write the number
Key ↓
What is the probability that all three balls drawn are of the same colour? Enter the answer correct to two decimal places.
Your answer:
Q5NAT4 Marks·Write the number
Key ↓
Let X denote the number of red balls selected. Find the value of P(X = 3 | X ≥ 1) Enter the answer correct to two decimal places.
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q6MCQ2 Marks·Choose one option
Key ↓
1. A0.2
2. B0.1
3. C1
4. D0.3
Q7MCQ3 Marks·Choose one option
Asked 3 times Key ↓
A survey of 800 students shows that 65% like reading and 50% like painting. If each student likes at least one of the two activities, how many students like painting but not reading?
1. A240
2. B400
3. C280
4. D120
Q8NAT2 Marks·Write the number
Key ↓
In a quiz competition, eight students are competing, each assigned a roll number from 1 to 8. What is the probability that only students with prime-numbered roll numbers (i.e., 2, 3, 5, 7) secure the top four ranks, in any order? Enter the answer correct to three decimal places.
Your answer:
Q9NAT3 Marks·Write the number
Asked 3 times Key ↓
A box C contains 3 white balls and 2 black balls, while box D contains 4 white balls and 3 black balls. One ball is randomly selected from box C and transferred to box D. After the transfer, one ball is drawn at random from box D. What is the probability that the ball drawn from box D is black? Enter the answer correct to three decimal places.
Your answer:
Read the passage below, then answer Q10–Q11
Based on the above data, answer the given subquestions.
Q10MCQ2 Marks·Choose one option
Key ↓
What is the probability that exactly 2 gold and 1 silver coin are drawn in the first draw?
1. A
2. B
3. C
4. D
Q11MCQ3 Marks·Choose one option
Key ↓
Given that the first draw results in 2 gold coins and 1 silver coin, what is the probability that the second draw results in exactly 2 silver coins and at least 1 gold coin?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q12–Q13
Based on the above data, answer the given subquestions.
Q12MSQ3 Marks·Choose all correct options
Key ↓
Which of the following option(s) is / are correct?
1. AEvents E_1 and E_2 are mutually exclusive.
2. BEvents E_1 and E_2 are independent.
3. CThere is only 1 favorable outcome for event E_2.
4. DAll of these
Q13NAT2 Marks·Write the number
Key ↓
How many panels include at least one Mathematics student?
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q14NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:

End Term · 13 Apr 2025 (AN)End Term

Q15NAT3 Marks·Write the number
Asked 3 times Key ↓
At a university, 60% of the students are enrolled in science programs, while 40% are enrolled in arts programs. Among science students, 25% participate in research projects, whereas 15% of arts students participate in research project. If a student is chosen at random, what is the probability that he/she participates in a research project? Enter the answer correct to two decimal places.
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Q16NAT2 Marks·Write the number
Asked 3 times Key ↓
In a survey of 100 people, 60 like tea, 40 like coffee, and 20 like both tea and coffee. What is the probability that a person chosen at random likes either tea or coffee? [Enter the correct answer up to 1 decimal place]
Your answer:
Q17MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
A jar contains 5 red balls and 7 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?
1. A
2. B
3. C
4. D

End Term · 22 Dec 2024 (AN)End Term

Q18NAT2 Marks·Write the number
Asked 3 times Key ↓
In a survey of 120 people, 70 like tea, 50 like coffee, and 30 like both tea and coffee. What is the probability that a person chosen at random likes either tea or coffee? [Enter the correct answer up to 1 decimal place]
Your answer:
Q19MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
A jar contains 6 red balls and 8 blue balls. Two balls are drawn without replacement. Let event A be the event that the first ball drawn is red, and event B be the event that the second ball drawn is blue. Which of the following statement(s) is(are) true?
1. A
2. B
3. C
4. D

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q10.17 to 0.21

Q20.73 to 0.79

Q30.7

Q40.14 to 0.2

Q50.02 to 0.08

Q6B

Q7C

Q80.011 to 0.017

Q90.422 to 0.428

Q10C

Q11B

Q12A, C

Q1319

Q140.51 to 0.57

Q150.18 to 0.24

Q160.8

Q17A, C

Q180.72 to 0.78

Q19A, C

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.