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Recent questions and answers in Probability
+11
votes
5
answers
1
TIFR2015A6
Ram has a fair coin, i.e., a toss of the coin results in either head or tail and each event happens with probability exactly half $(1/2)$. He repeatedly tosses the coin until he gets heads in two consecutive tosses. The expected number of coin tosses that Ram does is. $2$ $4$ $6$ $8$ None of the above.
answered
21 hours
ago
in
Probability
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tanishk1999
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tifr2015
expectation
+1
vote
1
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2
UGCNETDec2007II: 1
A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls are red and two are green ? $\large\frac{3}{7}$ $\large\frac{4}{7}$ $\large\frac{5}{7}$ $\large\frac{6}{7}$
answered
3 days
ago
in
Probability
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haralk10
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ugcnetdec2007ii
0
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1
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3
ISI2016MMA10
If $A_1, A_2, \dots , A_n$ are independent events with probabilities $p_1, p_2, \dots , p_n$ respectively, then $P( \cup_{i=1}^n A_i)$ equals $\Sigma_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: p_i$ $\Pi_{i=1}^n \: \: (1p_i)$ $1\Pi_{i=1}^n \: \: (1p_i)$
answered
Mar 19
in
Probability
by
SatyamK
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229
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43
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isi2016mmamma
probability
independentevents
+1
vote
2
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4
NIELIT DEC 2017 SETC 62
If a random coin is tossed 11 times then what is the probability that for 7th toss head appears exactly 4 times? A) 5/32 B) 15/128 C) 35/128 D) None of the options
answered
Mar 19
in
Probability
by
topper98
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589
points)

247
views
0
votes
2
answers
5
ISI2018MMA16
Consider a large village, where only two newspapers $P_1$ and $P_2$ are available to the families. It is known that the proportion of families not taking $P_1$ is $0.48$, not taking $P_2$ is $0.58$, taking only $P_2$ is $0.30$. The probability that a randomly chosen family from the village takes only $P_1$ is $0.24$ $0.28$ $0.40$ can not be determined
answered
Mar 1
in
Probability
by
kraken_wizard
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41
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137
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isi2018mma
engineeringmathematics
probability
0
votes
1
answer
6
TIFR2020A11
Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above
answered
Mar 1
in
Probability
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ankitgupta.1729
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18.1k
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48
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tifr2020
+3
votes
4
answers
7
GATE2020CS17
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
Feb 26
in
Probability
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immanujs
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gate2020cs
numericalanswers
probability
0
votes
1
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8
TIFR2020A7
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent of the other ... . $\dfrac{17}{2401}$ $\dfrac{48}{2401}$ $\dfrac{105}{2401}$ $\dfrac{175}{2401}$ $\dfrac{294}{2401}$
answered
Feb 26
in
Probability
by
ankitgupta.1729
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18.1k
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64
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tifr2020
engineeringmathematics
probability
independentevents
0
votes
1
answer
9
TIFR2020A10
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
answered
Feb 11
in
Probability
by
Sourajit25
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63
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tifr2020
engineeringmathematics
probability
0
votes
1
answer
10
TIFR2020A1
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
answered
Feb 11
in
Probability
by
neeraj_bhatt
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407
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47
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tifr2020
engineeringmathematics
probability
expectation
0
votes
0
answers
11
TIFR2020A4
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
asked
Feb 10
in
Probability
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Lakshman Patel RJIT
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61.3k
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35
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tifr2020
engineeringmathematics
probability
uniformdistribution
+2
votes
2
answers
12
UGCNETAUG2016III54
An experimental file server is up $75$% of the time and down for $25$% of the time due to bugs. How many times does this file server have to be replicated to give an availability of at least $99$% ? $2$ $4$ $8$ $16$
answered
Jan 23
in
Probability
by
Brian Mwangangi
(
17
points)

1.6k
views
ugcnetaug2016iii
probability
+20
votes
4
answers
13
GATE201421
The security system at an IT office is composed of $10$ computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed ... inspected are working. Let the probability that the system is deemed functional be denoted by p. Then $100$p = _____________.
answered
Jan 18
in
Probability
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gate20142
probability
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0
votes
1
answer
14
ISRO202056
For the distributions given below : Which of the following is correct for the above distributions ? Standard deviation of $A$ is significantly lower than standard deviation of $B$ Standard deviation of $A$ is slightly lower than standard deviation of $B$ Standard ... $B$ Standard deviation of $A$ is significantly higher than standard deviation of $B$
answered
Jan 13
in
Probability
by
Tuhin Dutta
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10.9k
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300
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isro2020
probability
standarddeviation
normal
+31
votes
4
answers
15
GATE2015337
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 $Pr[Y=0 \mid X_3 = 0] =$______.
answered
Jan 12
in
Probability
by
arjuno
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323
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3.7k
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gate20153
probability
randomvariable
normal
numericalanswers
+26
votes
5
answers
16
GATE201134
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 on the second ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$
answered
Jan 11
in
Probability
by
arjuno
(
323
points)

3.9k
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gate2011
probability
normal
+26
votes
8
answers
17
GATE200724
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
answered
Jan 11
in
Probability
by
arjuno
(
323
points)

5.1k
views
gate2007
probability
easy
uniformdistribution
+16
votes
5
answers
18
GATE200827
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer science the next ... , what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
answered
Jan 9
in
Probability
by
JashanArora
Loyal
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8.3k
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2.3k
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gate2008
probability
normal
+7
votes
5
answers
19
CMI2012A07
A man has three cats. At least one is male. What is the probability that all three are male? $\frac{1}{2}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{3}{8}$
answered
Jan 9
in
Probability
by
JashanArora
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8.3k
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550
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cmi2012
probability
0
votes
1
answer
20
ISI2016MMA9
Suppose $X$ and $Y$ are two independent random variables both following Poisson distribution with parameter $\lambda$. What is the value of $E(XY)^2$ ? $\lambda$ $2 \lambda$ $\lambda^2$ $4 \lambda^2$
answered
Jan 8
in
Probability
by
Ayan Kumar Pahari
Junior
(
553
points)

91
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isi2016mmamma
probability
randomvariable
poissondistribution
expectation
+16
votes
6
answers
21
TIFR2010B38
Suppose three coins are lying on a table, two of them with heads facing up and one with tails facing up. One coin is chosen at random and flipped. What is the probability that after the flip the majority of the coins(i.e., at least two of them) will have heads facing up? ... $\left(\frac{1}{4}\right)$ $\left(\frac{1}{4}+\frac{1}{8}\right)$ $\left(\frac{2}{3}\right)$
answered
Jan 8
in
Probability
by
Navneet Singh Tomar
Junior
(
927
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1.1k
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tifr2010
probability
binomialdistribution
+2
votes
1
answer
22
GO2019FLT153
A class of first year B.tech students is composed of four batches A, B, C and D, each consisting of $30$ students. It is found that the sessional marks of students in Engineering Drawing in batch C have a mean of $6.6$ and standard deviation of $2.3$. The mean and the standard ... Due to this, the marks of a student in batch C are changed from $8.5$ to $6.0$ $7.0$ $8.0$ $9.0$
answered
Jan 7
in
Probability
by
Dharmendra Tiwari
Junior
(
641
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242
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go2019flt1
statistics
probability
+6
votes
4
answers
23
ISRO201437
The probability that two friends are born in the same month is ____ ? 1/6 1/12 1/144 1/24
answered
Jan 6
in
Probability
by
Satbir
Boss
(
25.4k
points)

4k
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probability
isro2014
+1
vote
1
answer
24
NTA NET DEC 2018 Q88
A full joint distribution for the Toothache, Cavity and Catch is given in the table below : What is the probability of Cavity, given evidence of Toothache ? (a) <0.2, 0.8> (b) <0.6, 0.4> (c) <0.6, 0.8> (d) <0.4, 0.8>
answered
Dec 28, 2019
in
Probability
by
`JEET
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19.7k
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133
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conditionalprobability
+4
votes
4
answers
25
GATE201923
Two numbers are chosen independently and uniformly at random from the set $ [ 1, 2, \dots, 13]$. The probability (rounded off to $3$ decimal places ) that their $4bit$ (unsigned) binary representations have the same most significant bit is
answered
Dec 13, 2019
in
Probability
by
`JEET
Boss
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19.7k
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1.3k
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gate2019
probability
0
votes
1
answer
26
Normal Distribution
The median of a normal variate x with probablity dessity function f(x) = 1/(sigma*root(2*pi)*exp[{(xu)^2}/(2*sigma^2)] = ?
answered
Dec 11, 2019
in
Probability
by
cipherattack
(
19
points)

114
views
+6
votes
5
answers
27
TIFR2012A17
A spider is at the bottom of a cliff, and is $n$ inches from the top. Every step it takes brings it one inch closer to the top with probability $1/3$, and one inch away from the top with probability $2/3$, unless it is at the bottom in which case, it ... function of $n$? It will never reach the top. Linear in $n$. Polynomial in $n$. Exponential in $n$. Double exponential in $n$.
answered
Dec 3, 2019
in
Probability
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pritishc
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671
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tifr2012
probability
0
votes
1
answer
28
Probability Gravner 79.c
A random variable $X$ has the density function $f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$ (c) Determine the probability density function of $Y$ $=$ $X^2$
answered
Nov 28, 2019
in
Probability
by
Mk Utkarsh
Boss
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36.9k
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68
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probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
29
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (c) Determine EX and Var(X).
answered
Nov 27, 2019
in
Probability
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Mk Utkarsh
Boss
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36.9k
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44
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
30
Probability  Gravner69.b
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (b) Compute $P(1\leqslant X\leqslant 2)$
answered
Nov 27, 2019
in
Probability
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Mk Utkarsh
Boss
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36.9k
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40
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
31
Probability  Gravner69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
answered
Nov 27, 2019
in
Probability
by
Mk Utkarsh
Boss
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36.9k
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36
views
gravner
probability
engineeringmathematics
randomvariable
+23
votes
4
answers
32
GATE2006IT22
When a coin is tossed, the probability of getting a Head is $p, 0 < p < 1$. Let $N$ be the random variable denoting the number of tosses till the first Head appears, including the toss where the Head appears. Assuming that successive tosses are independent, the expected value of $N$ is $\dfrac{1}{p}$ $\dfrac{1}{(1  p)}$ $\dfrac{1}{p^{2}}$ $\dfrac{1}{(1  p^{2})}$
answered
Nov 26, 2019
in
Probability
by
Mk Utkarsh
Boss
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36.9k
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2.7k
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gate2006it
probability
binomialdistribution
expectation
normal
0
votes
2
answers
33
ISI2017DCG28
A basket contains some white and blue marbles. Two marbles are drawn randomly from the basket without replacement. The probability of selecting first a white and then a blue marble is $0.2$. The probability of selecting a white marble in the first draw is $0.5$. What is the ... blue marble in the second draw, given that the first marble drawn was white? $0.1$ $0.4$ $0.5$ $0.2$
answered
Nov 17, 2019
in
Probability
by
Yash4444
Junior
(
895
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77
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isi2017dcg
probability
ballsinbins
+1
vote
0
answers
34
Variation on Birthday Problem
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.
asked
Nov 12, 2019
in
Probability
by
Ayush Upadhyaya
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30.7k
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202
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probability
+14
votes
5
answers
35
TIFR2013A14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $\dfrac{1}{(2n)}$ $\dfrac{1}{[(6n)!]}$ $1  6^{n}$ $6^{n}$ None of the above.
answered
Nov 11, 2019
in
Probability
by
commenter commenter
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552
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tifr2013
probability
+14
votes
4
answers
36
GATE19942.6
The probability of an event $B$ is $P_1$. The probability that events $A$ and $B$ occur together is $P_2$ while the probability that $A$ and $\bar{B}$ occur together is $P_3$. The probability of the event $A$ in terms of $P_1, P_2$ and $P_3$ is _____________
answered
Nov 10, 2019
in
Probability
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amanc262
(
125
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1k
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gate1994
probability
normal
descriptive
conditionalprobability
+6
votes
4
answers
37
TIFR2013A17
A stick of unit length is broken into two at a point chosen at random. Then, the larger part of the stick is further divided into two parts in the ratio $4:3$. What is the probability that the three sticks that are left CANNOT form a triangle? $1/4$ $1/3$ $5/6$ $1/2$ $\log_{e}(2)/2$
answered
Nov 5, 2019
in
Probability
by
techbd123
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503
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tifr2013
probability
+17
votes
7
answers
38
GATE200552
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is: $\frac{1}{2^n}$ $1  \frac{1}{n}$ $\frac{1}{n!}$ $1  \frac{1}{2^n}$
answered
Nov 3, 2019
in
Probability
by
Utkarsh Pathak
Junior
(
555
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2.2k
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gate2005
probability
binomialdistribution
easy
+2
votes
2
answers
39
CMI2019A6
Suppose you alternate between throwing a normal sixsided fair die and tossing a fair coin. You start by throwing the die. What is the probability that you will see a $5$ on the die before you see tails on the coin? $\frac{1}{12}$ $\frac{1}{6}$ $\frac{2}{9}$ $\frac{2}{7}$
answered
Nov 3, 2019
in
Probability
by
techbd123
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3.7k
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153
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cmi2019
probability
+25
votes
4
answers
40
GATE2017119
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 ______________ .
answered
Nov 2, 2019
in
Probability
by
Satbir
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25.4k
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6.9k
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gate20171
probability
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normaldistribution
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