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Recent questions tagged probability
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GATE ECE 2021 | Question: 27
A box contains the following three coins. A fair coin with head on one face and tail on the other face. A coin with heads on both the faces. A coin with tails on both the faces. A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one ... getting a head in the second toss is $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
Arjun
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Probability and Statistics
Feb 20, 2021
by
Arjun
6.0k
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224
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gateec-2021
probability-and-statistics
probability
conditional-probability
1
vote
1
answer
2
GATE ECE 2020 | Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
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Probability and Statistics
Feb 13, 2020
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go_editor
1.9k
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185
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gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
0
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3
GATE ECE 2020 | Question: 54
$X$ is a random variable with uniform probability density function in the interval $[-2,\:10]$. For $Y=2X-6$, the conditional probability $P\left ( Y\leq 7\mid X\geq 5 \right )$ (rounded off to three decimal places) is __________.
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Probability and Statistics
Feb 13, 2020
by
go_editor
1.9k
points
79
views
gate2020-ec
numerical-answers
probability-and-statistics
probability
probability-density-function
uniform-distribution
0
votes
0
answers
4
GATE2016 EC-3: 3
The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _________
KUSHAGRA गुप्ता
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Probability and Statistics
Nov 21, 2019
by
KUSHAGRA गुप्ता
270
points
61
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gate2016-ec
probability
1
vote
0
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5
GATE2009 EC: 11
A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads. (A) $\left(\dfrac{1}{2}\right)^{2}$ (B) $^{10}C_2\left(\dfrac{1}{2}\right)^{2}$ (C) $\left(\dfrac{1}{2}\right)^{10}$ (D) $^{10}C_2\left(\dfrac{1}{2}\right)^{10}$
KUSHAGRA गुप्ता
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Probability and Statistics
Nov 21, 2019
by
KUSHAGRA गुप्ता
270
points
51
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gate2009-ec
probability
0
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6
GATE ECE 2019 | Question: 18
If $X$ and $Y$ are random variables such that $E\left[2X+Y\right]=0$ and $E\left[X+2Y\right]=33$, then $E\left[X\right]+E\left[Y\right]=$___________.
Arjun
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Probability and Statistics
Feb 12, 2019
by
Arjun
6.0k
points
84
views
gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
expectation
0
votes
0
answers
7
GATE ECE 2019 | Question: 20
Let $Z$ be an exponential random variable with mean $1$. That is, the cumulative distribution function of $Z$ is given by $F_{Z}(x)= \left\{\begin{matrix} 1-e^{-x}& \text{if}\: x \geq 0 \\ 0& \text{if}\: x< 0 \end{matrix}\right.$ Then $Pr\left(Z>2 \mid Z>1\right),$ rounded off to two decimal places, is equal to ___________.
Arjun
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Probability and Statistics
Feb 12, 2019
by
Arjun
6.0k
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169
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gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
0
votes
0
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8
GATE ECE 2019 | Question: 47
A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the random variable at the channel output is $Y=X+N$. The noise $N$ is ... probability of error $Pr[ \hat{X} \neq X].$ The minimum probability of error, rounded off to $1$ decimal place, is _________.
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Probability and Statistics
Feb 12, 2019
by
Arjun
6.0k
points
124
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gate2019-ec
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
0
votes
0
answers
9
GATE ECE 2016 Set 3 | Question: 3
The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _______
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Mar 28, 2018
by
Milicevic3306
15.8k
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112
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gate2016-ec-3
probability-and-statistics
probability
independent-events
0
votes
0
answers
10
GATE ECE 2016 Set 3 | Question: 22
An analog baseband signal, bandlimited to $100\ Hz$, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities $p_1 = p_4 = 0.125$ and $p_2 = p_3$. The information rate (bits/sec) of the message source is _______
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Control Systems
Mar 28, 2018
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Milicevic3306
15.8k
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58
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gate2016-ec-3
numerical-answers
control-systems
nyquist
probability
0
votes
0
answers
11
GATE ECE 2016 Set 3 | Question: 51
The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be in error is _______
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Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
84
views
gate2016-ec-3
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
12
GATE ECE 2016 Set 2 | Question: 21
A discrete memoryless source has an alphabet $\left \{ a_{1},a_{2}, a_{3},a_{4}\right \}$ with corresponding probabilities $\left \{ \frac{1}{2}, \frac{1}{4},\frac{1}{8},\frac{1}{8}\right \}.$ The minimum required average codeword length in bits to represent this source for error-free reconstruction is _________
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Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
73
views
gate2016-ec-2
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
13
GATE ECE 2016 Set 2 | Question: 28
Two random variables $X$ and $Y$ are distributed according to $f_{X,Y}(x,y)=\begin{cases} (x+y),& 0\leq x\leq 1,&0\leq y\leq 1\\ 0, & \text{otherwise.} \end{cases}$ The probability $P(X+Y\leq 1)$ is ________
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Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
99
views
gate2016-ec-2
numerical-answers
probability-and-statistics
probability
probability-density-function
0
votes
0
answers
14
GATE ECE 2016 Set 1 | GA Question: 6
A person moving through a tuberculosis prone zone has a $50 \%$ probability of becoming infected. However, only $30 \%$ of infected people develop the disease. What percentage of people moving through a tuberculosis prone zone remains infected but does not show symptoms of disease? $15$ $33$ $35$ $37$
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Quantitative Aptitude
Mar 28, 2018
by
Milicevic3306
15.8k
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45
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gate2016-ec-1
numerical-ability
probability
0
votes
0
answers
15
GATE ECE 2016 Set 1 | Question: 2
The second moment of a Poisson-distributed random variable is $2$. The mean of the random variable is _____
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Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
44
views
gate2016-ec-1
numerical-answers
probability-and-statistics
probability
poisson-distribution
random-variable
0
votes
0
answers
16
GATE ECE 2016 Set 1 | Question: 48
Consider a discrete memoryless source with alphabet $S = \{s_0,s_1,s_2,s_3,s_4, \dots \}$ and respective probabilities of occurence $P = \bigg\{ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots \bigg\}$. The entropy of the source (in bits) is _________
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Mar 28, 2018
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Milicevic3306
15.8k
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82
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gate2016-ec-1
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
17
GATE ECE 2015 Set 3 | Question: 27
A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The expected value of $X$ is _______.
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Mar 28, 2018
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38
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gate2015-ec-3
numerical-answers
probability-and-statistics
probability
expectation
0
votes
0
answers
18
GATE ECE 2015 Set 3 | Question: 52
A random binary wave $y(t)$ is given by $y(t) = \sum_{n = -\infty}^{\infty}X_{n}\:p(t-nT-\phi)$ where $p(t)=u(t)-u(t-T),u(t)$ is the unit step function and $\phi$ is an independent random variable with uniform distribution in $[0,T].$ ... $R_{yy}\left(\dfrac{3T}{4}\right) \underset{=}{\Delta} E\left[y(t)y\left(t-\dfrac{3T}{4}\right)\right]$ equals _________.
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Mar 28, 2018
by
Milicevic3306
15.8k
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55
views
gate2015-ec-3
numerical-answers
probability-and-statistics
probability
random-variable
uniform-distribution
0
votes
0
answers
19
GATE ECE 2015 Set 2 | GA Question: 5
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $1/6$ and that of Ramesh is $1/8$. What is the probability that only one of them will be selected? $47/48$ $1/4$ $13/48$ $35/48$
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Quantitative Aptitude
Mar 28, 2018
by
Milicevic3306
15.8k
points
49
views
gate2015-ec-2
numerical-ability
probability
0
votes
0
answers
20
GATE ECE 2015 Set 2 | Question: 29
Let the random variable $X$ represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of $X$ is _______.
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Mar 28, 2018
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Milicevic3306
15.8k
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41
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gate2015-ec-2
numerical-answers
probability-and-statistics
probability
random-variable
expectation
0
votes
0
answers
21
GATE ECE 2015 Set 2 | Question: 52
Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to $pq+(1-p)(1-q)$ $pq$ $p(1-q)$ $1-pq$
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Probability and Statistics
Mar 28, 2018
by
Milicevic3306
15.8k
points
39
views
gate2015-ec-2
probability-and-statistics
probability
random-variable
0
votes
0
answers
22
GATE ECE 2015 Set 1 | Question: 3
Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements is FALSE? $P(A \cap B) = P(A)P(B)$ $P(A \mid B) = P(A)$ $P(A \cup B) = P(A) + P(B)$ $P(\overline{A} \cap \overline{B} )= P(\overline{A})P(\overline{B})$
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Mar 28, 2018
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43
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gate2015-ec-1
probability-and-statistics
probability
independent-events
0
votes
0
answers
23
GATE ECE 2015 Set 1 | Question: 49
The input $X$ to the Binary Symmetric Channel (BSC) shown in the figure is $’1’$ with probability $0.8$. The cross-over probability is $1/7$. If the received bit $Y=0$, the conditional probability that $’1’$ was transmitted is ____________
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Mar 28, 2018
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15.8k
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91
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gate2015-ec-1
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
24
GATE ECE 2015 Set 1 | Question: 52
A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides for either $0$ or $1$ based on the received value $R$. It is given that the ... $0$ $1/12$ $1/9$ $1/6$
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15.8k
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75
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gate2015-ec-1
probability-and-statistics
probability
probability-density-function
0
votes
0
answers
25
GATE ECE 2014 Set 4 | Question: 27
Parcels from sender S to receiver R pass sequentially through two-post offices. Each post-office has a probability $\frac{1}{5}$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post office is _________
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Mar 26, 2018
by
Milicevic3306
15.8k
points
59
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gate2014-ec-4
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
26
GATE ECE 2014 Set 4 | Question: 50
Consider the $Z$-channel given in the figure. The input is $0$ or $1$ with equal probability. If the output is $0$, the probability that the input is also $0$ equals ___________
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Mar 26, 2018
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15.8k
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35
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gate2014-ec-4
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
27
GATE ECE 2014 Set 3 | GA Question: 10
A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is ________
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Quantitative Aptitude
Mar 26, 2018
by
Milicevic3306
15.8k
points
32
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gate2014-ec-3
numerical-ability
probability
numerical-answers
0
votes
0
answers
28
GATE ECE 2014 Set 3 | Question: 4
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is $0.067$ $0.073$ $0.082$ $0.091$
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Milicevic3306
15.8k
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49
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gate2014-ec-3
probability-and-statistics
probability
0
votes
0
answers
29
GATE ECE 2014 Set 3 | Question: 28
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
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Mar 26, 2018
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32
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gate2014-ec-3
probability-and-statistics
probability
expectation
numerical-answers
0
votes
0
answers
30
GATE ECE 2014 Set 3 | Question: 29
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1]$. The probability $P\left \{ X_{1}+X_{2}\leq X_{3}\right \}$ is _________.
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Mar 26, 2018
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Milicevic3306
15.8k
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67
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gate2014-ec-3
probability-and-statistics
probability
independent-events
random-variable
uniform-distribution
numerical-answers
0
votes
0
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31
GATE ECE 2014 Set 3 | Question: 52
A binary random variable $X$ takes the value of $1$ with probability $1/3$. $X$ is input to a cascade of $2$ independent identical binary symmetric channels (BSCs) each with crossover probability $1/2$. The output of BSCs are the random variables $Y_{1}$ and $Y_{2}$ as shown in the figure. The value of $H( Y_{1} )+H( Y_{2} )$ in bits is ______.
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Mar 26, 2018
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Milicevic3306
15.8k
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66
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gate2014-ec-3
probability-and-statistics
probability
numerical-answers
0
votes
0
answers
32
GATE ECE 2014 Set 2 | GA Question: 4
A regular die has six sides with numbers $1$ to $6$ marked on its sides. If a very large number of throws show the following frequencies of occurrence: $1 \rightarrow 0.167$; $2 \rightarrow 0.167$; $3 \rightarrow 0.152$; $4 \rightarrow 0.166$; $5 \rightarrow 0.168$; $6 \rightarrow 0.180$. We call this die irregular biased Gaussian insufficient
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Milicevic3306
15.8k
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39
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gate2014-ec-2
numerical-ability
probability
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0
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33
GATE ECE 2014 Set 2 | Question: 2
Let $X$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $100$. The expectation, $E[X]$, is ________.
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Mar 26, 2018
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15.8k
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46
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gate2014-ec-2
probability-and-statistics
probability
uniform-distribution
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numerical-answers
0
votes
0
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34
GATE ECE 2014 Set 2 | Question: 49
The input to a $1$ – bit quantizer is a random variable $X$ with pdf $f_{X}( x )= 2e^{-2x}$ for $x\geq 0$ and $f_{X} (x )= 0$ for $x< 0$. For outputs to be of equal probability, the quantizer threshold should be ______.
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54
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gate2014-ec-2
numerical-answers
probability-and-statistics
probability
probability-density-function
random-variable
0
votes
0
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35
GATE ECE 2014 Set 1 | GA Question: 10
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $1/4$ $1/3$ $1/2$ $2/3$
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Quantitative Aptitude
Mar 26, 2018
by
Milicevic3306
15.8k
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36
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gate2014-ec-1
numerical-ability
probability
1
vote
1
answer
36
GATE ECE 2014 Set 1 | Question: 2
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.
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Probability and Statistics
Mar 26, 2018
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Milicevic3306
15.8k
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377
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gate2014-ec-1
numerical-answers
probability-and-statistics
probability
0
votes
0
answers
37
GATE ECE 2014 Set 1 | Question: 5
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is the largest}\}$ is ________.
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Mar 26, 2018
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Milicevic3306
15.8k
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59
views
gate2014-ec-1
numerical-answers
probability-and-statistics
probability
uniform-distribution
0
votes
0
answers
38
GATE ECE 2014 Set 1 | Question: 49
Let $X$ be a real-valued random variable with $E[X]$ and $E[X^{2}]$ denoting the mean values of $X$ and $X^{2},$ respectively. The relation which always holds true is $(E[X])^{2}>E[X^{2}]$ $E[X^{2}]\geq (E[X])^{2}$ $E[X^{2}] = (E[X])^{2}$ $E[X^{2}] > (E[X])^{2}$
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Mar 26, 2018
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Milicevic3306
15.8k
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42
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gate2014-ec-1
probability-and-statistics
probability
random-variable
expectation
0
votes
0
answers
39
GATE ECE 2013 | Question: 65
What is the chance that a leap year, selected at random, will contain $53$ Saturdays? $2/7$ $3/7$ $1/7$ $5/7$
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Quantitative Aptitude
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Milicevic3306
15.8k
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52
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gate2013-ec
numerical-ability
probability
leap-year
0
votes
0
answers
40
GATE ECE 2013 | Question: 38
Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. Then, for all values of $x$ $F(x) - G(x) \leq 0$ $F(x) - G(x) \geq 0$ $(F(x) - G(x)) \cdot x\leq 0$ $(F(x) - G(x)) \cdot x\geq 0$
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Mar 26, 2018
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15.8k
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153
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gate2013-ec
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