The IIT Madras BS Statistics for Data Science I (Stats 1) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term: 15 questions for 40 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Consider the following events:
(A) Drawing a red card from a standard deck of 52 cards.
(B) Rolling a sum of 10 with two independent rolls of an unbiased die.
which of these events has the maximum probability?
A
B
Both have the same probability
Correct answer
A
In how many ways can 6 people be arranged in a line such that two specific people, A and B, must never be next to each other?
480
720
240
600
Correct answer
480
A company needs to select a team of 5 members from a group of 12 employees. Out of these, 3 specific roles need to be assigned: Team Leader, Manager, and Analyst. How many different ways can the team be selected and the roles allocated?
95040
47520
1320
4752
Correct answer
47520
In how many different ways can the letters of the word “AMERICA” be arranged such that the consonants always come together?
720
360
120
5040
Correct answer
360
Out of 6 boys and 4 girls, how many queues of 3 boys and 2 girls can be formed?
120
14400
1440
252
Correct answer
14400
Which of the following option(s) is(are) correct?
Probability values can be negative.
The probability of an event and its complement always add up to 0.
The probability of two independent events occurring simultaneously is the product of their individual probabilities.
The set of all possible outcomes of a random experiment is called sample space.
Correct answers
The probability of two independent events occurring simultaneously is the product of their individual probabilities.
The set of all possible outcomes of a random experiment is called sample space.
Correct answers
A box contains three distinct white balls, four distinct black balls, and three distinct red balls. Find the number of ways in which three balls can be drawn from the box so that all three drawn balls have different colors.
Correct answer: 36
Correct answer: 0.3
A card is randomly drawn from a standard deck of 52 playing cards. If the chosen card is known to be a face card (King, Queen, or Jack), what is the probability that it is also an Ace?
Correct answer: 0
The number of ways to arrange n + 1 objects in a line is equal to 6 times the number of ways to arrange n objects in a line. Find the value of n.
Correct answer: 5
In how many ways can 7 people be arranged around a circular table if one specific person must always occupy a fixed seat, which cannot be changed?
Correct answer: 120
There are 6 dark chocolates and 5 milk chocolates in a fridge. A person selects 3 chocolates from the fridge at random. Find the probability that among the chocolates drawn there is at least one chocolate of each type. Enter the answer correct to two decimal places.
Correct answer: 0.82 (accepted within ±0.03)
At a school, 30% of students are members of the Science Club, while 70% are members of the Art Club. Data indicates that the probability of passing a specific test, given that a student is in the Science Club, is 0.8, whereas the probability of passing the same test, given membership in the Art Club, is 0.4.
Based on the above data, answer the given subquestions.
What is the probability that a randomly selected student passes the test?
Enter the answer correct to two decimal places.
Correct answer: 0.52 (accepted within ±0.03)
At a school, 30% of students are members of the Science Club, while 70% are members of the Art Club. Data indicates that the probability of passing a specific test, given that a student is in the Science Club, is 0.8, whereas the probability of passing the same test, given membership in the Art Club, is 0.4.
Based on the above data, answer the given subquestions.
If a randomly selected student is known to have passed the test, what is the probability that this student is a member of the Science Club?
Enter the answer correct to two decimal places.
Correct answer: 0.46 (accepted within ±0.03)
