Recent questions tagged probability - GATE CSE Doubts

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PROBABILTY AND DISTRIBUTIONS
A elevator manufacturing company believes that 'X' is the amount of that can elevator withstand without any damage with is mean 100 and standard deviation 10. This elevator is used to lift the company staff persons with mean 5 and standard deviation 0.5. How many staff person would have to be in the elevator for the probability of No damage exceeds to 0.85.

asked 2 days ago in Mathematical Logic by Stanfordboi (6 points) | 7 views

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GATE2012-33 Video Solution
Suppose a fair six-sided 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 $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$

asked Apr 19 in Probability by admin (3.6k points) | 2 views

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GATE2012 CY: GA-7 Video Solution
$A$ and $B$ are friends. They decide to meet between 1:00 pm and 2:00 pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is $1/4$ $1/16$ $7/16$ $9/16$

asked Apr 19 in Numerical Ability by admin (3.6k points) | 2 views

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GATE2007-IT-58 Video Solution
A demand paging system takes $100$ time units to service a page fault and $300$ time units to replace a dirty page. Memory access time is $1$ time unit. The probability of a page fault is $p$ ... the average access time is $3$ time units. Then the value of $p$ is $0.194$ $0.233$ $0.514$ $0.981$

asked Apr 19 in Operating System by admin (3.6k points) | 1 view

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GATE2007-IT-28 Video Solution
Consider a hash function that distributes keys uniformly. The hash table size is $20$. After hashing of how many keys will the probability that any new key hashed collides with an existing one exceed $0.5$. $5$ $6$ $7$ $10$

asked Apr 19 in DS by admin (3.6k points) | 2 views

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GATE2017-1-19 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 ______________ .

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2014-1-2 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 ________ .

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2019-22 Video Solution
Two numbers are chosen independently and uniformly at random from the set $\{1,2,\ldots,13\}.$ The probability (rounded off to 3 decimal places) that their $4-bit$ (unsigned) binary representations have the same most significant bit is _______________.

asked Apr 19 in Digital Logic by admin (3.6k points) | 4 views

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GATE2005-IT-32 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 $3$ $4$ $5$ $6$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2014-3-40 Video Solution
Consider a hash table with $100$ slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first $3$ slots are unfilled after the first $3$ insertions? $(97 \times 97 \times 97) / 100^3$ $(99 \times 98 \times 97) / 100^3$ $(97 \times 96 \times 95) / 100^3$ $(97 \times 96 \times 95 / (3! \times 100^3)$

asked Apr 19 in DS by admin (3.6k points) | 1 view

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GATE1994-1.4, ISRO2017-2 Video Solution
Let $A$ and $B$ be any two arbitrary events, then, which one of the following is TRUE? $P (A \cap B) = P(A)P(B)$ $P (A \cup B) = P(A)+P(B)$ $P (A \mid B) = P(A \cap B)P(B)$ $P (A \cup B) \leq P(A) + P(B)$

asked Apr 19 in Probability by admin (3.6k points) | 3 views

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GATE2015-1-GA-10 Video Solution
The probabilities that a student passes in mathematics, physics and chemistry are $m,p$ and $c$ respectively. Of these subjects, the student has $75\%$ chance of passing in at least one, a $50\%$ chance of passing in at least two and a $40\%$ ... Only relation I is true. Only relation II is true. Relations II and III are true. Relations I and III are true.

asked Apr 19 in Numerical Ability by admin (3.6k points) | 1 view

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GATE2013-24 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? $\dfrac {1}{8}$ $1$ $7$ $8$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2010-27 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 19 in Probability by admin (3.6k points) | 1 view

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GATE2017-2-31 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

asked Apr 19 in Probability by admin (3.6k points) | 7 views

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GATE2017-2-48 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 ___.

asked Apr 19 in Probability by admin (3.6k points) | 2 views

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GATE2018-GA-10 Video Solution
A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment? Three green faces and four red faces. Four green faces and three red faces. Five green faces and two red faces. Six green faces and one red face

asked Apr 19 in Numerical Ability by admin (3.6k points) | 1 view

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GATE2008-29 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 $3$ $2$ $\sqrt{2}$ $1$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2007-24 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

asked Apr 19 in Probability by admin (3.6k points) | 2 views

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GATE2018-44 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 _____

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2019-47 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) _______

asked Apr 19 in Probability by admin (3.6k points) | 4 views

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GATE2001-2.4 Video Solution
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day? $\dfrac{1}{7^7}\\$ $\dfrac{1}{7^6}\\$ $\dfrac{1}{2^7}\\$ $\dfrac{7}{2^7}\\$

asked Apr 19 in Probability by admin (3.6k points) | 0 views

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GATE2004-54 Video Solution
$A$ and $B$ are the only two stations on an Ethernet. Each has a steady queue of frames to send. Both $A$ and $B$ attempt to transmit a frame, collide, and $A$ wins the first backoff race. At the end of this successful transmission by $A$, both $A$ and $B$ attempt to transmit and collide. The probability that $A$ wins the second backoff race is: $0.5$ $0.625$ $0.75$ $1.0$

asked Apr 19 in Computer Networks by admin (3.6k points) | 2 views

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GATE2017-2-26 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 ... $\left(\dfrac{5}{6}\right)$ $\left(\dfrac{7}{8}\right)$ $\left(\dfrac{11}{12}\right)$

asked Apr 19 in Probability by admin (3.6k points) | 3 views

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GATE2009-21 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 $3$? $0.453$ $0.468$ $0.485$ $0.492$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2016-1-29 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)

asked Apr 19 in Probability by admin (3.6k points) | 2 views

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GATE2004-IT-33 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 $\left(\dfrac{1}{\alpha + \beta}\right)$ $\min (\alpha, \beta)$ $\left(\dfrac{\alpha\beta}{\alpha + \beta}\right)$ $\alpha + \beta$

asked Apr 19 in Probability by admin (3.6k points) | 2 views

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GATE2017-2-GA-5 Video Solution
There are $3$ red socks, $4$ green socks and $3$ blue socks.You choose $2$ socks. The probability that they are of the same colour is $\dfrac{1}{5}$ $\dfrac{7}{30}$ $\dfrac{1}{4}$ $\dfrac{4}{15}$

asked Apr 19 in Numerical Ability by admin (3.6k points) | 1 view

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GATE2016-1-04 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 _________.

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2019-20 Video Solution
An array of $25$ distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to $2$ decimal places) is ________

asked Apr 19 in Algorithms by admin (3.6k points) | 1 view

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GATE2007-65 Video Solution
There are $n$ stations in slotted LAN. Each station attempts to transmit with a probability $p$ in each time slot. What is the probability that ONLY one station transmits in a given time slot? $np(1-p)^{n-1}$ $(1-p)^{n-1}$ $p(1-p)^{n-1}$ $1-(1-p)^{n-1}$

asked Apr 19 in Computer Networks by admin (3.6k points) | 2 views

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GATE2011-34 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 ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$

asked Apr 19 in Probability by admin (3.6k points) | 3 views

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GATE2018-15 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 ____

asked Apr 19 in Probability by admin (3.6k points) | 8 views

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GATE2012-21 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 $0.75$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2007-IT-65 Video Solution
Consider a selection of the form $\sigma_{A\leq 100} (r)$, where $r$ is a relation with $1000$ tuples. Assume that the attribute values for $A$ among the tuples are uniformly distributed in the interval $[0, 500].$ Which one of the following options is the best estimate of the number of tuples returned by the given selection query ? $50$ $100$ $150$ $200$

asked Apr 19 in Databases by admin (3.6k points) | 1 view

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GATE2015-3-37 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 $Pr[Y=0 \mid X_3 = 0] =$______.

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2017-1-GA-5 Video Solution
The probability that a $k$-digit number does NOT contain the digits $0, 5,$ or $9$ is $0.3^{k}$ $0.6^{k}$ $0.7^{k}$ $0.9^{k}$

asked Apr 19 in Numerical Ability by admin (3.6k points) | 2 views

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GATE1995-1.18 Video Solution
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$ $\left(\dfrac{9}{10}\right)^{3}$ $\dfrac{27}{75}$ $\dfrac{18}{25}$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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GATE2003-60, ISRO2007-45 Video Solution
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ ... $\int_0^t f_1(x)f_2(t-x)dx$ $\max\{f_1(t),f_2(t)\}$

asked Apr 19 in Probability by admin (3.6k points) | 2 views

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GATE2013-2 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? $\dfrac{8}{(2e^{3})}$ $\dfrac{9}{(2e^{3})}$ $\dfrac{17}{(2e^{3})}$ $\dfrac{26}{(2e^{3})}$

asked Apr 19 in Probability by admin (3.6k points) | 1 view

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