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IITM BS Week 8 Statistics 1 Questions | Prasnya
Statistics 1 > Week 8
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36Q
01
There are two stores, A and B, which sell t-shirts on the market. Store A has stock of
n
n
n
red and
2
2
2
black t-shirts, and store B has stock of
2
2
2
red and
n
n
n
black t-shirts. One of the stores is selected at random and two t-shirts are purchased without replacement from that store. Given that both the t-shirts purchased are red, the probability that they were purchased from store A is
6
7
\frac{6}{7}
7
6
. Find the value of
n
n
n
.
Numerical
MEDIUM
5 marks
06 April 2026
02
Three independent draws are made from a standard deck of
52
52
52
playing cards, with replacement and reshuffling between each draw. Which of the following statements is/are correct?
Multiple correct
EASY
3 marks
06 April 2026
03
A bakery sells bread, cake, and pastry each day. Of the total items sold,
40
%
40\%
40%
are bread,
30
%
30\%
30%
are cake, and
25
%
25\%
25%
are pastry. Each individual item has a
6
%
6\%
6%
probability of being defective, either stale or burnt, independent of its type. One item is selected at random from the total items sold that day. Define the events
S
S
S
: the selected item is stale or burnt, and
C
C
C
: the selected item is cake. Which of the following options is/are correct?
Multiple correct
MEDIUM
4 marks
06 April 2026
04
Find the probability that the committee contains exactly one girl, given that it contains at least one boy.
Comprehension
MEDIUM
2 marks
06 April 2026
05
Find the value of
P
(
B
∣
(
A
∪
C
)
)
P(B|(A\cup C))
P
(
B
∣
(
A
∪
C
))
. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
06 April 2026
06
If
P
(
C
)
=
0.3
P(C)=0.3
P
(
C
)
=
0.3
,
P
(
A
∪
B
)
=
0.6
P(A \cup B)=0.6
P
(
A
∪
B
)
=
0.6
and
P
(
A
∪
B
∪
C
)
=
0.8
P(A \cup B \cup C)=0.8
P
(
A
∪
B
∪
C
)
=
0.8
, what is the value of
P
(
(
A
∪
B
)
∩
C
)
P((A \cup B) \cap C)
P
((
A
∪
B
)
∩
C
)
?
Single correct
EASY
2 marks
03 August 2025
07
A box
C
C
C
contains
3
3
3
white balls and
2
2
2
black balls, while box
D
D
D
contains
4
4
4
white balls and
3
3
3
black balls. One ball is randomly selected from box
C
C
C
and transferred to box
D
D
D
. After the transfer, one ball is drawn at random from box
D
D
D
. What is the probability that the ball drawn from box
D
D
D
is black? Enter the answer correct to three decimal places.
Numerical
MEDIUM
3 marks
03 August 2025
08
Given that the first draw results in
2
2
2
gold coins and
1
1
1
silver coin, what is the probability that the second draw results in exactly
2
2
2
silver coins and at least
1
1
1
gold coin?
Comprehension
MEDIUM
3 marks
03 August 2025
09
Which of the following option(s) is/are correct?
Comprehension
MEDIUM
3 marks
03 August 2025
10
Consider an experiment of rolling a fair four-sided die twice where all possible outcomes are equally likely. Define the events
A
A
A
: first roll results in
1
1
1
,
B
B
B
: sum of the two rolls is
7
7
7
, and
C
C
C
: second roll results in
2
2
2
. Which among the following statements are true?
Multiple correct
MEDIUM
4 marks
16 March 2025
11
A card is randomly drawn from a standard deck of
52
52
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?
Numerical
EASY
2 marks
16 March 2025
12
What is the probability that a randomly selected student passes the test? Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
16 March 2025
13
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.
Comprehension
MEDIUM
2 marks
16 March 2025
14
An urn
B
1
B_1
B
1
contains
2
2
2
white and
3
3
3
black chips and another urn
B
2
B_2
B
2
contains
3
3
3
white and
4
4
4
black chips. One urn is selected at random and a chip is drawn from it. If the chip drawn is found black, find the probability that the urn chosen was
B
1
B_1
B
1
. Enter the answer correct up to
2
2
2
decimal places.
Numerical
MEDIUM
4 marks
01 December 2024
15
In a school with
120
120
120
students,
90
90
90
students are enrolled in Math,
50
50
50
students are enrolled in Science, and
30
30
30
students are enrolled in both Math and Science. If a student is randomly selected, what is the probability that he/she is enrolled in Science given that he/she is enrolled in Math?
Single correct
EASY
3 marks
01 December 2024
16
Which of the following options is/are correct?
Multiple correct
MEDIUM
3 marks
01 December 2024
17
Which of the following option(s) is/are true?
Multiple correct
EASY
2 marks
04 August 2024
18
Find the probability that a randomly chosen passenger gets a taxi with engine issues. Enter the answer correct to three decimal places.
Comprehension
MEDIUM
3 marks
04 August 2024
19
Given that a passenger gets a taxi with engine issues, find the probability that the passenger took a ride with the Green taxi company. Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
04 August 2024
20
Are the events
E
1
E_1
E
1
and
E
2
E_2
E
2
independent?
Comprehension
EASY
2 marks
04 August 2024
21
Which of the following option(s) is/are correct?
Multiple correct
MEDIUM
3 marks
24 March 2024
22
What is the probability that both are boys given that at least one is a boy? Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
24 March 2024
23
What is the probability that co-education will be introduced in the college?
Comprehension
MEDIUM
3 marks
24 March 2024
24
If co-education has been introduced in the college, then what is the probability that
X
X
X
is principal? Enter the answer correct to two decimal places.
Comprehension
MEDIUM
2 marks
24 March 2024
25
A fair die is rolled twice and a fair coin is tossed twice. Define events
A
A
A
and
B
B
B
as follows:
A
A
A
: a three appears on the die twice.
B
B
B
: a head appears on the coin twice. Find the value of
P
(
A
∩
B
)
P(A\cap B)
P
(
A
∩
B
)
.
Single correct
MEDIUM
3 marks
03 December 2023
26
Consider an experiment of rolling a fair four-sided die twice where all the possible outcomes are equally likely. Define the events:
A
=
A=
A
=
first roll results in a
1
1
1
,
B
=
B=
B
=
sum of the two rolls is
7
7
7
, and
C
=
C=
C
=
second roll results in a
2
2
2
. Which among the following statements are true?
Multiple correct
HARD
4 marks
03 December 2023
27
What is the probability that Suman will win the colour TV?
Comprehension
MEDIUM
4 marks
03 December 2023
28
If she wins a colour TV, then what is the probability that candy was from bag
B
1
B_1
B
1
? Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
03 December 2023
29
A person is randomly picked from this group. What is the probability that the person is a female, given that the person's reaction is favourable to the new gadget? Enter the answer correct to two decimal places.
Comprehension
MEDIUM
3 marks
03 December 2023
30
Ajay speaks truth in
50
%
50\%
50%
cases, while Vijay speaks truth in
90
%
90\%
90%
cases. What is the probability that Ajay and Vijay will contradict in stating the same fact?
Numerical
MEDIUM
4 marks
06 August 2023
31
A blood test indicates the presence of Amyotrophic lateral sclerosis (ALS)
93
%
93\%
93%
of the time when ALS is actually present. The same test indicates the presence of ALS
0.5
%
0.5\%
0.5%
of the time when ALS is not actually present. One percent of the population actually has ALS. Calculate the probability that a person actually has ALS given that the test indicates the presence of ALS. Enter your answer correct to two decimal places.
Numerical
HARD
5 marks
06 August 2023
32
Parcels from sender
S
S
S
to receiver
R
R
R
pass sequentially through two post offices. The first post office has probability
1
/
8
1/8
1/8
of losing an incoming parcel, and the second post office has probability
1
/
5
1/5
1/5
of losing an incoming parcel, independently of all other parcels. Given that the parcel is lost, find the probability that it was lost by the second post office. Enter the answer correct to 2 decimal accuracy.
Numerical
MEDIUM
4 marks
02 April 2023
33
An urn contains cards numbered
100
100
100
to
500
500
500
. One card is drawn at random. Define events:
E
1
E_1
E
1
: the number on the card is greater than
150
150
150
but less than or equal to
200
200
200
;
E
2
E_2
E
2
: the number is greater than or equal to
106
106
106
but less than
156
156
156
;
E
3
E_3
E
3
: the number is greater than
60
60
60
but less than or equal to
110
110
110
. Which statement(s) is/are true?
Multiple correct
HARD
4 marks
20 November 2022
34
A box contains
15
15
15
numbered balls such that red coloured balls are numbered
1
1
1
to
8
8
8
and black coloured balls are numbered
9
9
9
to
15
15
15
. If a randomly chosen ball is even numbered, then what is the probability that the selected ball is of red colour? Enter the answer correct to two decimal accuracy.
Numerical
MEDIUM
4 marks
20 November 2022
35
What is the probability that an email is detected as spam? Enter the answer correct to two decimal accuracy.
Comprehension
MEDIUM
3 marks
20 November 2022
36
If the email is detected as spam, then what is the probability that it is in fact a non-spam email? Enter the answer correct to two decimal accuracy.
Comprehension
MEDIUM
4 marks
20 November 2022
Showing 36 questions.
Complete question index for this section:
Question 1 (integer):
Question 2 (multiple):
Question 3 (multiple):
Question 4 (comprehension):
Question 5 (comprehension):
Question 6 (single):
Question 7 (integer):
Question 8 (comprehension):
Question 9 (comprehension):
Question 10 (multiple):
Question 11 (integer):
Question 12 (comprehension):
Question 13 (comprehension):
Question 14 (integer):
Question 15 (single):
Question 16 (multiple):
Question 17 (multiple):
Question 18 (comprehension):
Question 19 (comprehension):
Question 20 (comprehension):
Question 21 (multiple):
Question 22 (comprehension):
Question 23 (comprehension):
Question 24 (comprehension):
Question 25 (single):
Question 26 (multiple):
Question 27 (comprehension):
Question 28 (comprehension):
Question 29 (comprehension):
Question 30 (integer):
Question 31 (integer):
Question 32 (integer):
Question 33 (multiple):
Question 34 (integer):
Question 35 (comprehension):
Question 36 (comprehension):
