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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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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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#A First Course In Probability Sheldon Ross #self_doubt
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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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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
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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 ______.
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Apr 23
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gate2020cs
numericalanswers
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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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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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gate20171
probability
numericalanswers
normaldistribution
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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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gate20141
probability
uniformdistribution
expectation
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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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gate2005it
probability
binomialdistribution
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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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gate1994
probability
conditionalprobability
normal
isro2017
videosolution
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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
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gate2013
probability
expectation
normal
videosolution
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GATE201027 Video Solution
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
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gate2010
probability
normal
videosolution
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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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gate20172
probability
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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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gate20172
expectation
poissondistribution
numericalanswers
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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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gate2008
randomvariable
normaldistribution
probability
normal
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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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Probability
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gate2007
probability
easy
uniformdistribution
videosolution
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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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gate2018
probability
conditionalprobability
numericalanswers
videosolution
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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
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gate2019
numericalanswers
engineeringmathematics
probability
uniformdistribution
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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
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Probability
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gate2001
probability
normal
videosolution
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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
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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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Probability
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gate2009
probability
normal
videosolution
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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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gate20161
probability
normal
numericalanswers
videosolution
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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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gate2004it
probability
exponentialdistribution
randomvariable
normal
videosolution
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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
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Probability
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gate20161
probability
normal
numericalability
numericalanswers
continuousdistribution
videosolution
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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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Probability
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gate2011
probability
normal
videosolution
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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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gate2018
probability
normal
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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
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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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gate20153
probability
randomvariable
normal
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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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gate1995
probability
normal
videosolution
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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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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
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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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gate2004
probability
uniformdistribution
expectation
normal
videosolution
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GATE2007IT57 Video Solution
In a multiuser operating system on an average, $20$ requests are made to use a particular resource per hour. The arrival of requests follows a Poisson distribution. The probability that either one, three or five requests are made in $45$ ... $6.9 \times 10^3 \times e^{20}$ $1.02 \times 10^3 \times e^{20}$
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gate2007it
probability
poissondistribution
normal
videosolution
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GATE19952.14 Video Solution
A bag contains $10$ white balls and $15$ black balls. Two balls are drawn in succession. The probability that one of them is black and the other is white is: $\frac{2}{3}$ $\frac{4}{5}$ $\frac{1}{2}$ $\frac{1}{3}$
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Probability
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gate1995
probability
normal
videosolution
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GATE2016205 Video Solution
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.
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gate20162
probability
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normal
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videosolution
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GATE20022.16 Video Solution
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is $\frac{1}{16}$ $\frac{1}{8}$ $\frac{7}{8}$ $\frac{15}{16}$
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gate2002
probability
easy
videosolution
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GATE2014148 Video Solution
Four fair sixsided dice are rolled. The probability that the sum of the results being $22$ is $\dfrac{X}{1296}$. The value of $X$ is _______
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gate20141
probability
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GATE200512, ISRO200964 Video Solution
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is : $f(ba)$ $f(b)  f(a)$ $\int\limits_a^b f(x) dx$ $\int\limits_a^b xf (x)dx$
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gate2005
probability
randomvariable
easy
isro2009
videosolution
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GATE20033 Video Solution
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
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gate2003
probability
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conditionalprobability
videosolution
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