The IIT Madras BS Statistics for Data Science I (Stats 1) Quiz 2 paper sat on 13 Mar 2022, in the January 2022 term, set QPE1: 19 questions for 50 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.
Answer the given subquestion.
From a box containing 5 dark chocolates and 3 milk chocolates, 3 chocolates are to be selected randomly without replacement. In how many ways can the chocolates be selected such that at least one dark chocolate is selected?
Correct answer: 55
Answer the given subquestion.
Select the steps from the following options, that you will use for the selection of chocolates. Note: This question is optional. We will check your answer to this question if you make a mistake in the previous one.
Selection of chocolates will occur simultaneously.
Selection of chocolates will not occur simultaneously.
With replacement.
Without replacement.
Order matters.
Order does not matter.
Correct answers
Selection of chocolates will occur simultaneously.
Without replacement.
Order does not matter.
Suppose Ankit has 2 empty pen boxes which are to be filled by 3 pens. In how many ways can the boxes be filled with pens such that none of the box remains empty?
18
3² − 2
19
2³ − 2
Correct answer
2³ − 2
20790
50820
25410
1210
Correct answer
25410
Consider the following events:
A: Throwing a 4 with one unbiased die.
B: Throwing a sum of 8 with two independent rolls of an unbiased die.
Which of these events has the least probability?
A
B
Both have the same probability
Correct answer
B
X contains observations of the speed of a car and Y contains the observations of the speed of another car, and it is noted that each observation of Y is 2 times each observation of X. If the sample variance of X is 64, then calculate the sample covariance between X and Y ?
128
256
64
0
Correct answer
128
If we have observations 30, 25, 35, 40 and 45, then find the population variance of the data?
62.5
50
40
35
Correct answer
50
Answer the given subquestions.
How many words, with or without meaning, can be formed using the letters of the word ’MADRAS’ (without repetition), such that the alphabet ’D’ occupies the 3*^(rd)* position (moving from left to right) in each of the words formed?
Correct answer: 60
Answer the given subquestions.
Select the steps from the following options, that you will use for forming words using letters of the word ’MADRAS’.
Note: This question is optional. We will check your answer to this question if you make a mistake in the previous one.
Selection of letters will occur simultaneously.
Selection of letters will not occur simultaneously.
With replacement.
Without replacement.
Order matters.
Order does not matter.
Correct answers
Selection of letters will occur simultaneously.
Without replacement.
Order matters.
Correct answer
A salesman wants to sell two products, ’A’ and ’B’. The chances of him selling the products ’A’ and ’B’ are 30% and 70% respectively. The two products can be sold independently. Given that he is able to sell at least one product, what is the probability that the product A has been sold? (Enter the answer correct to 2 decimal accuracy)
Correct answer: 0.38 (accepted within ±0.04)
Urn ’A’ contains 3 white and 5 black balls. 4 balls are transferred to an empty urn B from urn A. From urn B, a ball is drawn at random and is found to be white. What is the probability that out of 4 balls transferred 3 are white and 1 is black?
Correct answer
What is the probability that the team will be given direct entry to the knock-out stage in the next tournament?(Enter the answer correct to 2 decimal accuracy)
Correct answer: 0.51 (accepted within ±0.04)
If the team is given direct entry to the knock-out stage in the next tournament, what is the probability that the team A has won the current tournament?(Enter the answer correct to 2 decimal accuracy)
Correct answer: 0.26 (accepted within ±0.04)
The Statistics department of a college has a batch of 50 students. Of the total number of students in the batch, 28 are boys and the rest are girls. If two students are selected at random (without replacement) to represent the college in a competition, then find the probability that the first student selected is a boy and the second one selected is a girl?
(Enter the answer correct to 2 decimal places)
Correct answer: 0.25 (accepted within ±0.04)
Answer the given subquestions.
Rohit wants to create a 4-digit numerical password for his mobile phone. In how many ways, can he create a 4-digit numerical password between 4000 and 10000 with digits 0, 2, 3, 4, 5, 6 if no digit is repeated?
Correct answer: 180
Answer the given subquestions.
Select the steps from the following options,that you will use to create 4-digit numerical password using the given digits.
Note: This question is optional. We will check your answer to this question if you make a mistake in the previous one.
Selection of digits will occur simultaneously.
Selection of digits will not occur simultaneously.
With replacement.
Without replacement.
Order matters.
Order does not matter.
Correct answers
Selection of digits will occur simultaneously.
Without replacement.
Order matters.
Answer the given subquestions.
In how many ways can, 6 team members including a captain, vice-captain and a coach, sit around a circular table, when the captain is to sit on one side of the coach and the vice-captain on the other side?
Correct answer: 12
Answer the given subquestions.
Select the steps from the following options, that you will use for arranging team members around a circular table.
Note: This question is optional. We will check your answer to this question if you make a mistake in the previous one.
Selection of team members will occur simultaneously.
Selection of team members will not occur simultaneously.
With replacement.
Without replacement.
Order matters.
Order does not matter.
Correct answers
Selection of team members will occur simultaneously.
Without replacement.
Order matters.
