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Recent questions tagged probability
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In rural Ireland, a century ago, the students had to form a line. The student at the front of the line would be asked to spell a word. If he spelled it correctly, he was allowed to sit down. If not, he received a whack on the hand with a switch and was sent to the end of the line. Suppose that a student could spell correctly 70% of the words in the lesson. What is the probability that the student would be able to sit down before receiving four whacks on the hand? Assume that the master chose the words to be spelled randomly and independently.
tim20
asked
in
Algorithms
Feb 23
by
tim20
58
views
algorithms
probability
0
votes
4
answers
2
GATE DS&AI 2024 | GA Question: 7
The probability of a boy or a girl being born is $1 / 2$. For a family having only three children, what is the probability of having two girls and one boy? $3 / 8$ $1 / 8$ $1 / 4$ $1 / 2$
Arjun
asked
in
Quantitative Aptitude
Feb 17
by
Arjun
2.1k
views
gate-ds-ai-2024
quantitative-aptitude
probability
0
votes
1
answer
3
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
Arjun
asked
in
Probability
Feb 17
by
Arjun
1.1k
views
gate-ds-ai-2024
probability
0
votes
1
answer
4
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? $2$ $4$ $6$ $8$
Arjun
asked
in
Probability
Feb 17
by
Arjun
924
views
gate-ds-ai-2024
probability
0
votes
1
answer
5
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).
Arjun
asked
in
Probability
Feb 17
by
Arjun
573
views
gate-ds-ai-2024
numerical-answers
probability
random-variable
0
votes
1
answer
6
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).
Arjun
asked
in
Probability
Feb 17
by
Arjun
609
views
gate-ds-ai-2024
numerical-answers
probability
1
vote
1
answer
7
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 $\frac{1}{324}$ $\frac{5}{324}$ $\frac{7}{324}$ $\frac{11}{324}$
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.6k
views
gatecse2024-set2
probability
1
vote
3
answers
8
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 $\bar{x}, \bar{y}, \bar{z}$ ... $\bar{z} \leq \bar{x} \bar{y}$ $\bar{z} \geq \bar{x} \bar{y}$ $\bar{z} \leq \bar{x}$
Arjun
asked
in
Probability
Feb 16
by
Arjun
2.1k
views
gatecse2024-set2
probability
random-variable
0
votes
1
answer
9
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 $Y$
Arjun
asked
in
Probability
Feb 16
by
Arjun
2.1k
views
gatecse2024-set1
probability
1
vote
1
answer
10
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
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.7k
views
gatecse2024-set1
multiple-selects
probability
0
votes
2
answers
11
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 ___________.
Arjun
asked
in
Probability
Feb 16
by
Arjun
1.7k
views
gatecse2024-set1
numerical-answers
probability
2
votes
2
answers
12
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
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
440
views
goclasses2024-mockgate-14
probability
conditional-probability
1-mark
2
votes
1
answer
13
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
asked
in
Probability
Feb 5
by
GO Classes
321
views
goclasses2024-mockgate-14
probability
uniform-distribution
2-marks
2
votes
1
answer
14
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 \(5E(x) = V(x)\).
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
275
views
gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
0
votes
1
answer
15
Memory Based GATE DA 2024 | Question: 8
In a family with three children, determine the probability of having two boys and one girl.
GO Classes
asked
in
Quantitative Aptitude
Feb 5
by
GO Classes
238
views
gate2024-da-memory-based
goclasses
quantitative-aptitude
probability
numerical-answers
0
votes
2
answers
16
Memory Based GATE DA 2024 | Question: 9
Three coins are tossed. Let $T$ be the event of getting at least two heads, and $S$ be the event of getting at least two tails. Determine the value of $\mathrm{P}(\mathrm{T} \cap \mathrm{S})$.
GO Classes
asked
in
Quantitative Aptitude
Feb 5
by
GO Classes
199
views
gate2024-da-memory-based
goclasses
quantitative-aptitude
probability
numerical-answers
0
votes
0
answers
17
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
asked
in
Probability
Feb 5
by
GO Classes
158
views
gate2024-da-memory-based
goclasses
probability
normal-distribution
numerical-answers
0
votes
2
answers
18
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.
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
432
views
gate2024-da-memory-based
goclasses
probability
conditional-probability
numerical-answers
0
votes
1
answer
19
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: $\mathrm{P}({\mathrm{T}})=0.4$ ... $\mathrm{P}(\mathrm{T}|\mathrm{S})$.
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
161
views
gate2024-da-memory-based
goclasses
probability
conditional-probability
numerical-answers
0
votes
0
answers
20
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
asked
in
Probability
Feb 5
by
GO Classes
164
views
gate2024-da-memory-based
goclasses
probability
expectation
numerical-answers
0
votes
0
answers
21
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
asked
in
Probability
Feb 5
by
GO Classes
124
views
gate2024-da-memory-based
goclasses
probability
conditional-probability
0
votes
0
answers
22
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
asked
in
Probability
Feb 5
by
GO Classes
80
views
gate2024-da-memory-based
goclasses
probability
statistics
0
votes
1
answer
23
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 $P(x \geq y)$
GO Classes
asked
in
Probability
Feb 5
by
GO Classes
194
views
gate2024-da-memory-based
goclasses
probability
random-variable
uniform-distribution
numerical-answers
0
votes
0
answers
24
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
asked
in
Probability
Feb 5
by
GO Classes
128
views
gate2024-da-memory-based
goclasses
probability
poisson-distribution
normal-distribution
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