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Recent questions and answers in Probability
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Combinatorics and Probability
Six people including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "A precedes B in the queue". (Again this event does not mention C or other people in the queue. It happens when A is ... not require that B is the next after A, some people could be between A and B.) What is the probability of this event?
answered
1 day
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Probability
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Ashutosh07091999
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25
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conditionalprobability
permutation&combination
discrete_maths
probability
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Combinatorics and Probability
Six people, including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "B is between A and C in the queue". What is its probability? (The order of A and C can be arbitrary, but B should be between them).
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1 day
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in
Probability
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aryashah2k
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11
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3
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permutation&combination
conditionalprobability
discrete_maths
probability
#combinatory
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1
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MIT OCW Probability Assignment 02
1. Most mornings, Victor checks the weather report before deciding whether to carry an umbrella. If the forecast is rain, the probability of actually having rain that day is 80%. On the other hand, if the forecast is no rain, the probability ... rain if it was during the winter? What is the probability that the forecast was rain if it was during the summer?
answered
Jul 24
in
Probability
by
aryashah2k
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11
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14
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conditionalprobability
0
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0
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TCS MockVita 2020 , Lazy Student
There is a test of Algorithms. Teacher provides a question bank consisting of N questions and guarantees all the questions in the test will be from this question bank. Due to lack of time and his laziness, Codu could only practice M questions. There ... problems. Codu can't solve the question he didn't practice. What is the probability that Codu will pass the test?
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Jul 2
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Probability
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pravincesingh
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6
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51
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#probability
#tcs
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0
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What are the relevant chapter in Gravner for Probability ?
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Jun 26
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Probability
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Ram_81
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8
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3
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gravner
#probability
0
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3
answers
Expectation : Self Doubt
There is a bag containing 5 white and 5 black balls. You repeat the following experiment till you see a white ball : take a ball uniformly at random out of the bag. If it is white, stop. Otherwise, put it back in the bag. What is the expected number of times you will need to draw a ball from the bag ?
answered
Jun 22
in
Probability
by
Nikhil_dhama
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87
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103
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discrete_maths
expectation
0
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1
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#self doubt why is the method wrong to solve the problem
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Jun 13
in
Probability
by
Himanshu Kumar Gupta
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14
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14
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#combinatory
#cards
#probability
0
votes
1
answer
GATE GURU TEST SERIES MATHS
A cancer institute has a testing methodology. The methodology produces 95% positive result, also 10% rate of falsepositive(i..e showing a non cancer person as a cancer affected patient). If there are 0.5% of the people have cancer. Suppose a person is classified as a disease affected person, what is the probability that the person is really have cancer? _______________
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May 31
in
Probability
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shaktipratap
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9
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138
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engineeringmaths
0
votes
0
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A first course in probability by Ross
Let A denote the event that the midtown temperature in Los Angeles is 70◦F, and let B denote the event that the midtown temperature in New York is 70◦F. Also, let C denote the event that the maximum of the midtown temperatures in New York and in Los ... ,P(B) =.4, and P(C) = .2, find the probability that the minimum of the two midtown temperatures is 70◦F.
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May 21
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Probability
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Neelam_$ingh_222
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12
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7
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0
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0
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#A First Course In Probability Sheldon Ross #self_doubt
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May 21
in
Probability
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Neelam_$ingh_222
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12
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5
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#selfdoubt
#probability
0
votes
0
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A first course in probability by Ross
A basketball team consists of 6 frontcourt and 4 backcourt players. If players are divided into roommates at random, what is the probability that there will be exactly two roommate pairs made up of a backcourt and a frontcourt player?
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May 21
in
Probability
by
Neelam_$ingh_222
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12
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7
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#probability
0
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0
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A first course in probability
Let A denote the event that the midtown temperature in Los Angeles is 70◦F, and let B denote the event that the midtown temperature in New York is 70◦F. Also, let C denote the event that the maximum of the midtown temperatures in New York and in Los Angeles is ... ,P(B) = .4, and P(C) = .2, find the probability that the minimum of the two midtown temperatures is 70◦F.
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May 21
in
Probability
by
Neelam_$ingh_222
(
12
points)

9
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#probability
+1
vote
1
answer
GATE2020CS17 Video Solution
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.
answered
Apr 23
in
Probability
by
amitkhurana512
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189
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8
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gate2020cs
numericalanswers
probability
videosolution
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0
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GATE201233 Video Solution
Suppose a fair sixsided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
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Apr 18
in
Probability
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admin
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3.6k
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5
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gate2012
probability
conditionalprobability
normal
videosolution
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GATE2017119 Video Solution
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
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Apr 18
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Probability
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gate20171
probability
numericalanswers
normaldistribution
videosolution
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0
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GATE201412 Video Solution
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
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Apr 18
in
Probability
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3.6k
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3
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gate20141
probability
uniformdistribution
expectation
numericalanswers
normal
videosolution
0
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0
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GATE2005IT32 Video Solution
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
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Apr 18
in
Probability
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3.6k
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4
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gate2005it
probability
binomialdistribution
expectation
normal
videosolution
0
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0
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GATE19941.4, ISRO20172 Video Solution
Let $A$ and $B$ be any two arbitrary events, then, which one of the following is TRUE? $P (A \cap B) = P(A)P(B)$ $P (A \cup B) = P(A)+P(B)$ $P (A \mid B) = P(A \cap B)P(B)$ $P (A \cup B) \leq P(A) + P(B)$
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Apr 18
in
Probability
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gate1994
probability
conditionalprobability
normal
isro2017
videosolution
0
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0
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GATE201324 Video Solution
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is $\dfrac{1}{2}.$ What is the expected number of unordered cycles of length three? $\dfrac {1}{8}$ $1$ $7$ $8$
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Apr 18
in
Probability
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admin
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3.6k
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5
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gate2013
probability
expectation
normal
videosolution
0
votes
0
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GATE201027 Video Solution
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
asked
Apr 18
in
Probability
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admin
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3.6k
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5
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gate2010
probability
normal
videosolution
0
votes
0
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GATE2017231 Video Solution
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain discrete ... . The expectation of $Y$ is $N \beta(1\beta)$ $N \beta$ $N (1\beta)$ Not expressible in terms of $N$ and $\beta$ alone
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Probability
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gate20172
probability
randomvariable
videosolution
0
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0
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GATE2017248 Video Solution
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
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Apr 18
in
Probability
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2
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gate20172
expectation
poissondistribution
numericalanswers
probability
videosolution
0
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0
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GATE200829 Video Solution
Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $1$ and variance unknown. If $P (X ≤ 1) = P (Y ≥ 2)$ , the standard deviation of $Y$ is $3$ $2$ $\sqrt{2}$ $1$
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Apr 18
in
Probability
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gate2008
randomvariable
normaldistribution
probability
normal
videosolution
0
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0
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GATE200724 Video Solution
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
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Apr 18
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Probability
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4
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gate2007
probability
easy
uniformdistribution
videosolution
0
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0
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GATE201844 Video Solution
Consider Guwahati, (G) and Delhi (D) whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ and $P(L_G)$ ... , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____
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Apr 18
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Probability
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gate2018
probability
conditionalprobability
numericalanswers
videosolution
0
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0
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GATE201947 Video Solution
Suppose $Y$ is distributed uniformly in the open interval $(1,6)$. The probability that the polynomial $3x^2 +6xY+3Y+6$ has only real roots is (rounded off to $1$ decimal place) _______
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Apr 18
in
Probability
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gate2019
numericalanswers
engineeringmathematics
probability
uniformdistribution
videosolution
0
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0
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GATE20012.4 Video Solution
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day? $\dfrac{1}{7^7}\\$ $\dfrac{1}{7^6}\\$ $\dfrac{1}{2^7}\\$ $\dfrac{7}{2^7}\\$
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Apr 18
in
Probability
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admin
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gate2001
probability
normal
videosolution
0
votes
0
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GATE2017226 Video Solution
$P$ and $Q$ are considering to apply for a job. The probability that $P$ applies for the job is $\dfrac{1}{4},$ the probability that $P$ applies for the job given that $Q$ applies for the job is $\dfrac{1}{2},$ and the probability that $Q$ applies for the job ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$
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Apr 18
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Probability
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gate20172
probability
conditionalprobability
videosolution
0
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0
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GATE200921 Video Solution
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability ... following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
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Apr 18
in
Probability
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admin
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2
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gate2009
probability
normal
videosolution
0
votes
0
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GATE2016129 Video Solution
Consider the following experiment. Step 1. Flip a fair coin twice. Step 2. If the outcomes are (TAILS, HEADS) then output $Y$ and stop. Step 3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output $N$ and stop. Step 4. If the ... (TAILS, TAILS), then go to Step 1. The probability that the output of the experiment is $Y$ is (up to two decimal places)
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Apr 18
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Probability
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gate20161
probability
normal
numericalanswers
videosolution
0
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0
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GATE2004IT33 Video Solution
Let $X$ and $Y$ be two exponentially distributed and independent random variables with mean $α$ and $β$, respectively. If $Z$ = min $(X, Y)$, then the mean of $Z$ is given by $\left(\dfrac{1}{\alpha + \beta}\right)$ $\min (\alpha, \beta)$ $\left(\dfrac{\alpha\beta}{\alpha + \beta}\right)$ $\alpha + \beta$
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Apr 18
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Probability
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gate2004it
probability
exponentialdistribution
randomvariable
normal
videosolution
0
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0
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GATE2016104 Video Solution
A probability density function on the interval $[a, 1]$ is given by $1/x^{2}$ and outside this interval the value of the function is zero. The value of $a$ is _________.
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Apr 18
in
Probability
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gate20161
probability
normal
numericalability
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GATE201134 Video Solution
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$
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Apr 18
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Probability
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gate2011
probability
normal
videosolution
0
votes
0
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GATE201815 Video Solution
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
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Apr 18
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Probability
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gate2018
probability
normal
numericalanswers
videosolution
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GATE201221 Video Solution
Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and $+1$ are $0$ and $0.5$ $0$ and $1$ $0.5$ and $1$ $0.25$ and $0.75$
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Apr 18
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Probability
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gate2012
probability
randomvariable
easy
videosolution
0
votes
0
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GATE2015337 Video Solution
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} \text{ for } i = 1, 2, 3$. Define another random variable $Y = X_1X_2 \oplus X_3$, where $\oplus$ denotes XOR. Then $Pr[Y=0 \mid X_3 = 0] =$______.
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Apr 18
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Probability
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gate20153
probability
randomvariable
normal
numericalanswers
videosolution
0
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GATE19951.18 Video Solution
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$ $\left(\dfrac{9}{10}\right)^{3}$ $\dfrac{27}{75}$ $\dfrac{18}{25}$
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Apr 18
in
Probability
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gate1995
probability
normal
videosolution
0
votes
0
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GATE200360, ISRO200745 Video Solution
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ ... $\int_0^t f_1(x)f_2(tx)dx$ $\max\{f_1(t),f_2(t)\}$
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Apr 18
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Probability
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gate2003
probability
normal
isro2007
videosolution
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GATE20132 Video Solution
Suppose $p$ is the number of cars per minute passing through a certain road junction between $5$ PM and $6$ PM, and $p$ has a Poisson distribution with mean $3$. What is the probability of observing fewer than $3$ cars during any given minute in this interval? $\dfrac{8}{(2e^{3})}$ $\dfrac{9}{(2e^{3})}$ $\dfrac{17}{(2e^{3})}$ $\dfrac{26}{(2e^{3})}$
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Probability
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gate2013
probability
poissondistribution
normal
videosolution
0
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GATE200480 Video Solution
A point is randomly selected with uniform probability in the $XY$ plane within the rectangle with corners at $(0,0), (1,0), (1,2)$ and $(0,2).$ If $p$ is the length of the position vector of the point, the expected value of $p^{2}$ is $\left(\dfrac{2}{3}\right)$ $\quad 1$ $\left(\dfrac{4}{3}\right)$ $\left(\dfrac{5}{3}\right)$
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Apr 18
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Probability
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gate2004
probability
uniformdistribution
expectation
normal
videosolution
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