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Recent questions and answers in Probability
7
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3
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1
Mathematics GATE 2011 probability
A fair die is tossed two times. the probability that 2nd toss results in value greater than first toss is ?
Creatorpk
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gate-ec
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16
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2
TIFR CSE 2014 | Part A | Question: 17
A fair dice (with faces numbered $1, . . . , 6$) is independently rolled repeatedly. Let $X$ denote the number of rolls till an even number is seen and let $Y$ denote the number of rolls till $3$ is seen. Evaluate $E(Y |X = 2)$. $6\frac{5}{6}$ $6$ $5\frac{1}{2}$ $6\frac{1}{3}$ $5\frac{2}{3}$
Priyam Garg
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Probability
Feb 25
by
Priyam Garg
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tifr2014
expectation
19
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7
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3
TIFR CSE 2013 | Part A | Question: 6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$
Priyam Garg
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Probability
Feb 25
by
Priyam Garg
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tifr2013
probability
conditional-probability
9
votes
5
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4
TIFR CSE 2013 | Part A | Question: 17
A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$. What is the probability that the three sticks that are left CANNOT form a triangle? $1/4$ $1/3$ $5/6$ $1/2$ $\log_{e}(2)/2$
Priyam Garg
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Probability
Feb 24
by
Priyam Garg
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tifr2013
probability
25
votes
7
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5
TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$
Priyam Garg
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Probability
Feb 23
by
Priyam Garg
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tifr2011
probability
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23
votes
5
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6
TIFR CSE 2012 | Part A | Question: 20
There are $1000$ balls in a bag, of which $900$ are black and $100$ are white. I randomly draw $100$ balls from the bag. What is the probability that the $101$st ball will be black? $9/10$ More than $9/10$ but less than $1$. Less than $9/10$ but more than $0$. $0$ $1$
Priyam Garg
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Probability
Feb 19
by
Priyam Garg
2.8k
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tifr2012
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1
vote
3
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7
GATE CSE 2024 | Set 2 | Question: 34
Let $x$ and $y$ be random variables, not necessarily independent, that take real values in the interval $[0,1]$. Let $z=x y$ and let the mean values of $x, y, z$ be $\bar{x}, \bar{y}, \bar{z}$ ... $\bar{z} \leq \bar{x} \bar{y}$ $\bar{z} \geq \bar{x} \bar{y}$ $\bar{z} \leq \bar{x}$
Argharupa Adhikary
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Probability
Feb 18
by
Argharupa Adhikary
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0
votes
1
answer
8
GATE DS&AI 2024 | Question: 48
Consider two events $T$ and $S$. Let $\bar{T}$ denote the complement of the event $T$. The probability associated with different events are given as follows: \[ P(\bar{T})=0.6, \quad P(S \mid T)=0.3, \quad P(S \mid \bar{T})=0.6 \] Then, $P(T \mid S)$ is ( ... P(S \mid T)=0.3, \quad P(S \mid \bar{T})=0.6 \] Then, $P(T \mid S)$ is (rounded off to two decimal places).
shishir__roy
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Probability
Feb 17
by
shishir__roy
609
views
gate-ds-ai-2024
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1
vote
1
answer
9
GATE CSE 2024 | Set 1 | Question: 17
Let $A$ and $B$ be two events in a probability space with $P(A)=0.3, P(B)=0.5$, and $P(A \cap B)=0.1$. Which of the following statements is/are TRUE? The two events $A$ and $B$ are independent $P(A \cup B)=0.7$ ... $B$ $P\left(A^c \cap B^c\right)=0.4$, where $A^c$ and $B^c$ are the complements of the events $A$ and $B$, respectively
malaviya_parth
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Probability
Feb 17
by
malaviya_parth
1.7k
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multiple-selects
probability
0
votes
2
answers
10
GATE CSE 2024 | Set 1 | Question: 53
A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to $3$ decimal places) that both balls drawn are red is ___________.
shishir__roy
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in
Probability
Feb 17
by
shishir__roy
1.7k
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gatecse2024-set1
numerical-answers
probability
0
votes
1
answer
11
GATE DS&AI 2024 | Question: 47
Let $X$ be a random variable exponentially distributed with parameter $\lambda>0$. The probability density function of $X$ is given by: \[ f_{X}(x)=\left\{\begin{array}{ll} \lambda e^{-\lambda x}, \quad x \geq 0 \\ 0, & \text ... $X$, respectively, the value of $\lambda$ is (rounded off to one decimal place).
NarutoUzumaki
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Probability
Feb 17
by
NarutoUzumaki
573
views
gate-ds-ai-2024
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random-variable
1
vote
1
answer
12
GATE CSE 2024 | Set 2 | Question: 8
When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers $(i.e., 1, 2, 3, 4, 5, \text{and } 6)$ is $\frac{1}{324}$ $\frac{5}{324}$ $\frac{7}{324}$ $\frac{11}{324}$
Deepak Poonia
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Probability
Feb 17
by
Deepak Poonia
1.6k
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gatecse2024-set2
probability
0
votes
1
answer
13
GATE DS&AI 2024 | Question: 1
Consider the following statements: The mean and variance of a Poisson random variable are equal. For a standard normal random variable, the mean is zero and the variance is one. Which ONE of the following options is correct? Both $\text{(i)}$ and $\text{(ii)}$ are true ... $\text{(i)}$ is false Both $\text{(i)}$ and $\text{(ii)}$ are false
NarutoUzumaki
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in
Probability
Feb 17
by
NarutoUzumaki
1.1k
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gate-ds-ai-2024
probability
0
votes
1
answer
14
GATE CSE 2024 | Set 1 | Question: 4
Consider a permutation sampled uniformly at random from the set of all permutations of $\{1,2,3, \cdots, n\}$ for some $n \geq 4$. Let $X$ be the event that $1$ occurs before $2$ in the permutation, and $Y$ the event that $3$ occurs before ... The events $X$ and $Y$ are independent Either event $X$ or $Y$ must occur Event $X$ is more likely than event $Y$
shishir__roy
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in
Probability
Feb 17
by
shishir__roy
2.1k
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gatecse2024-set1
probability
0
votes
1
answer
15
GATE DS&AI 2024 | Question: 26
A fair six-sided die (with faces numbered $1,2,3,4,5,6$ ) is repeatedly thrown independently. What is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$ A fair six-sided die ( ... is the expected number of times the die is thrown until two consecutive throws of even numbers are seen? $2$ $4$ $6$ $8$
ankitgupta.1729
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Probability
Feb 17
by
ankitgupta.1729
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views
gate-ds-ai-2024
probability
2
votes
2
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16
JEST 2019
Three dice are rolled independently. Probability of obtaining the difference from largest and smallest number as exactly 4 :
Priyam Garg
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in
Probability
Feb 11
by
Priyam Garg
489
views
jest
probability
2
votes
2
answers
17
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 21
Suppose we have events $A, B$ in a sample space. And we know that $\mathrm{P}(\mathrm{A})=0.3, \mathrm{P}\left(\mathrm{B} \mid \mathrm{A}^c\right)=0.25, \mathrm{P}(\mathrm{B} \mid \mathrm{A})=0.45$. What is $\mathrm{P}\left(\mathrm{A}^c \mid \mathrm{B}\right) ?$ 0.75 0.55 0.2 0.56
chidambareswar23
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in
Probability
Feb 7
by
chidambareswar23
440
views
goclasses2024-mockgate-14
probability
conditional-probability
1-mark
0
votes
1
answer
18
Memory Based GATE DA 2024 | Question: 42
Consider two random variables, (x) and (y), each following a uniform distribution. Specifically, (x) is uniformly distributed over the interval ([1, 3]), and (y) is uniformly distributed over the interval ([2, 4]). What will be $P(x \geq y)$
RahulVerma3
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in
Probability
Feb 6
by
RahulVerma3
194
views
gate2024-da-memory-based
goclasses
probability
random-variable
uniform-distribution
numerical-answers
0
votes
2
answers
19
Memory Based GATE DA 2024 | Question: 13
A fair six-sided die is thrown repeatedly. Find the expected number of throws until two consecutive throws show even numbers.
Mumuksh29
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in
Probability
Feb 5
by
Mumuksh29
432
views
gate2024-da-memory-based
goclasses
probability
conditional-probability
numerical-answers
0
votes
1
answer
20
Memory Based GATE DA 2024 | Question: 14
Consider two events $\mathrm{T}$ and $\mathrm{S}$. Let $\overline{\mathrm{T}}$ denote the complement of event $\mathrm{T}$. The probabilities associated with different events are given as follows: $\mathrm{P}({\mathrm{T}})=0.4$ ... $\mathrm{P}(\mathrm{T}|\mathrm{S})$.
Mumuksh29
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Probability
Feb 5
by
Mumuksh29
161
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gate2024-da-memory-based
goclasses
probability
conditional-probability
numerical-answers
2
votes
1
answer
21
Memory Based GATE DA 2024 | Question: 1
Consider the probability density function \(f(x) = \lambda e^{-\lambda x}\) for \(x \geq 0\) and \(\lambda > 0\). Determine the value of \(\lambda\) such that \(5E(x) = V(x)\).
Mrityudoot
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in
Probability
Feb 5
by
Mrityudoot
275
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gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
2
votes
1
answer
22
GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 48
Consider the quadratic equation $x^2+\dfrac{x}{2}+c=0$, where $c$ is chosen uniformly randomly from the interval $[0,1]$. What is the probability that the given quadratic equation has a real solution? The solutions of $a x^2+b x+c=0$ are given by $x=\dfrac{-b \pm \sqrt{b^2-4 a c}}{2a}$. $1 / 2$ $1 / 4$ $1 / 8$ $1 / 16$
GO Classes
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Probability
Feb 5
by
GO Classes
320
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goclasses2024-mockgate-14
probability
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2-marks
0
votes
0
answers
23
Memory Based GATE DA 2024 | Question: 11
Consider a dataset with a raw score \(x = 75\), a mean \(\mu = 70\), and a standard deviation \(\sigma = 5\). Calculate the Z-score using the formula \(z = \frac{x - \mu}{\sigma}\).
GO Classes
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Feb 5
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GO Classes
158
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gate2024-da-memory-based
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0
votes
0
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24
Memory Based GATE DA 2024 | Question: 15
Consider the joint probability density function given by: $ f(x, y)= \begin{cases} 2xy & \text{if } 0 < x < 2 \text{ and } 0 < y < x \\ 0 & \text{otherwise} \end{cases} $ \noindent Determine the conditional expectation $E(Y | X = 1.5)$.
GO Classes
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Probability
Feb 5
by
GO Classes
164
views
gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
0
votes
0
answers
25
Memory Based GATE DA 2024 | Question: 35
Conditional probability \[ \begin{aligned} & \mathrm{P}(\mathrm{U}, \mathrm{V}, \mathrm{W}, \mathrm{X}, \mathrm{Y}) & = \mathrm{P}(\mathrm{U}) \cdot \mathrm{P}(\mathrm{V}) \cdot \mathrm{P}(\mathrm{W} / \mathrm{U}, \mathrm{V}) \cdot \mathrm{P}(\mathrm{X} / \mathrm{W}) \cdot \mathrm{P}(\mathrm{Y} / \mathrm{W}) \end{aligned} \]
GO Classes
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Probability
Feb 5
by
GO Classes
124
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gate2024-da-memory-based
goclasses
probability
conditional-probability
0
votes
0
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26
Memory Based GATE DA 2024 | Question: 41
Consider two random variables, $x$ and $y$, defined as follows: \[ x = \begin{cases} 1 & \text{if HH } \\ 0 & \text{otherwise} \end{cases} \] \[ y = \begin{cases} 1 & \text{if at least one head} \\ 0 & \text{otherwise} \end{cases} \] What is the covariance between $x$ and $y?$
GO Classes
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GO Classes
80
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goclasses
probability
statistics
0
votes
0
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27
Memory Based GATE DA 2024 | Question: 44
Consider the statements below related to probability distributions: \textbf{(S1):} For a Poisson distribution, the mean and variance are equal. \textbf{(S2):} For a standard normal distribution, the mean is 0, and the variance is 1. Which of the following ... true. S1 is true, but S2 is false. S1 is false, but S2 is true. Both S1 and S2 are false.
GO Classes
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Feb 5
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GO Classes
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goclasses
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2
votes
3
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28
Probability
In a certain group of computer personnel, 65% have insufficient knowledge of hardware, 45% have inadequate idea of software and 70% are in either one (or) both of the two categories. What is the percentage of people who knpw software among those who have a sufficient knowledge of hardware? 0.35/0.3 0.3/0.35 0.3 0.35
Sbrjt
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Probability
Feb 4
by
Sbrjt
2.3k
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probability
6
votes
1
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29
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 12
Let $x$ be a random variable possessing the probability density function $ f(x)= \begin{cases}c x & , x \in[0,10] \\ 0 & , \text { otherwise }\end{cases} $ where $c \in \mathbb{R}$. The probability that $x \in[1,2]$ is ______. $\dfrac{1}{100}$ $\dfrac{3}{100}$ $\dfrac{5}{100}$ $\dfrac{7}{100}$
SankarVinayak
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in
Probability
Jan 29
by
SankarVinayak
425
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goclasses2024-mockgate-13
goclasses
probability
random-variable
1-mark
4
votes
1
answer
30
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 44
Football teams $T_1$ and $T_2$ play two games against each other in the Premier League. It is assumed that the outcomes of the two games are independent of each other. The probabilities of $T_1$ winning, drawing and losing against $T_2$ ... What will be the value of $P(X=Y)?$ $1 / 3$ $13 / 36$ $1 / 36$ $1 / 18$
GO Classes
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in
Probability
Jan 28
by
GO Classes
421
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goclasses2024-mockgate-13
goclasses
probability
conditional-probability
2-marks
7
votes
2
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31
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 6
A college has $10$ (non-overlapping) time slots for its courses, and assigns courses to time slots randomly and independently. A student randomly chooses $3$ of the courses to enroll in. What is the probability that there is a conflict in the student's schedule? (answer upto $2$ decimals)
krishnajsw
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in
Probability
Jan 21
by
krishnajsw
765
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goclasses2024-mockgate-12
goclasses
numerical-answers
probability
independent-events
1-mark
6
votes
1
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32
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 36
Let $A, B, C$ be events such that $P(A)=P(B)=P(C)=0.5, P(A \cap B)=0.3, P(A \cap C)=0$. Which of the following is/are true? $P(A \cup B)=0.75$ $P(A \cup C)=1$ $P(B \cap C)=0.23$ $P(B \cup C)=0.9$
GO Classes
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in
Probability
Jan 21
by
GO Classes
787
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goclasses2024-mockgate-12
goclasses
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2-marks
36
votes
7
answers
33
GATE CSE 2011 | Question: 18
If the difference between the expectation of the square of a random variable $\left(E\left[X^2\right]\right)$ and the square of the expectation of the random variable $\left(E\left[X\right]\right)^2$ is denoted by $R$, then $R=0$ $R<0$ $R\geq 0$ $R > 0$
yuyutsu
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Probability
Jan 19
by
yuyutsu
8.8k
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gatecse-2011
probability
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3
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1
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34
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 28
Suppose that $X$ and $Y$ are independent random variables such that each is equal to $0$ with probability $.5$ and $1$ with probability $.5.$ Find $P(X+Y \leq 1)?$ (Answer up to $2$ decimals)
GauravRajpurohit
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Probability
Jan 14
by
GauravRajpurohit
476
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goclasses2024-mockgate-11
goclasses
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8
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4
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35
GATE CSE 2023 | Question: 43
Consider a random experiment where two fair coins are tossed. Let $A$ be the event that denotes $\text{HEAD}$ on both the throws, $B$ be the event that denotes $\text{HEAD}$ on the first throw, and $C$ be the event that denotes $\text{HEAD}$ on the ... . $A$ and $C$ are independent. $B$ and $C$ are independent. $\operatorname{Prob}(B \mid C)=\operatorname{Prob}(B)$
Priyam Garg
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Probability
Jan 13
by
Priyam Garg
6.8k
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gatecse-2023
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independent-events
multiple-selects
2-marks
4
votes
1
answer
36
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 29
You have three coins in your pocket, two fair ones but the third biased with the probability of heads $p$ and tails $1-p$. One coin selected at random drops to the floor, landing heads up. How likely is it that it is one of the fair coins? $1 / \mathrm{p}$ $1 /(1+p)$ $p /(1+p)$ $(1+p) / p$
GO Classes
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Jan 13
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GO Classes
420
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goclasses2024-mockgate-11
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1-mark
0
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0
answers
37
Madeeasy 2024 full length test 3
Can anyone please help me solve this question or explain the formula used in the solution part of the same?
VinayBhojwani
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in
Probability
Jan 13
by
VinayBhojwani
134
views
0
votes
1
answer
38
GATE 2016 | MATHS | Q-33
Suppose \( X \) and \( Y \) are two random variables such that \( aX + bY \) is a normal random variable for all \( a, b \) in \( \mathbf{R} \). Consider the following statements P, Q, R, and S: (P) : \( X \) is a standard normal random variable. (Q) ... 0. Which of the above statements ALWAYS hold TRUE? (A) both P and Q (B) both Q and R (C) both Q and S (D) both P and S
rajveer43
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in
Probability
Jan 11
by
rajveer43
101
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statistics
probability
0
votes
0
answers
39
GATE 2018 | MATH | Q-64
Let \(X_1\) and \(X_2\) be independent geometric random variables with the same probability mass function given by \(P(X = k) = p(1 - p)^{k-1}\), \(k = 1, 2, \ldots\). Then the value of \(P(X_1 = 2 | X_1 + X_2 = 4)\) correct up to three decimal places is____________
rajveer43
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Probability
Jan 11
by
rajveer43
97
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probability
statistics
0
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0
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40
GATE 2018 | MATHS | Q-63
Let $X$ be the number of heads in 4 tosses of a fair coin by Person 1 and let $Y$ be the number of heads in 4 tosses of a fair coin by Person 2. Assume that all the tosses are independent. Then the value of $P(X = Y )$ correct up to three decimal places is_________
rajveer43
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Probability
Jan 11
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rajveer43
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