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Recent questions and answers in Probability
+18
votes
4
answers
1
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
2 days
ago
in
Probability
by
Kushagra गुप्ता
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4k
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3.7k
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gate20142
probability
numericalanswers
normal
0
votes
1
answer
2
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
6 days
ago
in
Probability
by
Tuhin Dutta
Boss
(
10.5k
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153
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isro2020
probability
standarddeviation
normal
+29
votes
4
answers
3
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
(
275
points)

3.3k
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gate20153
probability
randomvariable
normal
numericalanswers
+23
votes
5
answers
4
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
(
275
points)

3.6k
views
gate2011
probability
normal
+24
votes
8
answers
5
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
(
275
points)

4.7k
views
gate2007
probability
easy
uniformdistribution
+15
votes
5
answers
6
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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6.2k
points)

2.2k
views
gate2008
probability
normal
+6
votes
5
answers
7
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
Loyal
(
6.2k
points)

501
views
cmi2012
probability
0
votes
1
answer
8
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
(
323
points)

58
views
isi2016mmamma
probability
randomvariable
poissondistribution
expectation
+13
votes
6
answers
9
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
(
735
points)

1k
views
tifr2010
probability
binomialdistribution
+2
votes
1
answer
10
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
(
629
points)

202
views
go2019flt1
statistics
probability
+6
votes
4
answers
11
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
(
23.8k
points)

3.9k
views
probability
isro2014
+1
vote
1
answer
12
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
Boss
(
18.9k
points)

119
views
conditionalprobability
+3
votes
4
answers
13
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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18.9k
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1.1k
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gate2019
probability
0
votes
1
answer
14
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)

99
views
+5
votes
5
answers
15
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
by
pritishc
Active
(
1.9k
points)

642
views
tifr2012
probability
0
votes
1
answer
16
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
(
36.4k
points)

58
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
17
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
by
Mk Utkarsh
Boss
(
36.4k
points)

35
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
18
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
by
Mk Utkarsh
Boss
(
36.4k
points)

30
views
probability
gravner
engineeringmathematics
randomvariable
0
votes
1
answer
19
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
(
36.4k
points)

26
views
gravner
probability
engineeringmathematics
randomvariable
+21
votes
4
answers
20
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
(
36.4k
points)

2.5k
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gate2006it
probability
binomialdistribution
expectation
normal
0
votes
2
answers
21
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
(
833
points)

58
views
isi2017dcg
probability
ballsinbins
+1
vote
0
answers
22
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
Boss
(
29k
points)

171
views
probability
+12
votes
5
answers
23
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
Active
(
1.5k
points)

532
views
tifr2013
probability
+13
votes
4
answers
24
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
by
amanc262
(
25
points)

976
views
gate1994
probability
normal
descriptive
conditionalprobability
+5
votes
4
answers
25
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
Active
(
3.5k
points)

480
views
tifr2013
probability
+16
votes
7
answers
26
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
(
495
points)

2k
views
gate2005
probability
binomialdistribution
easy
+2
votes
2
answers
27
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
Active
(
3.5k
points)

120
views
cmi2019
probability
+22
votes
4
answers
28
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
Boss
(
23.8k
points)

6.3k
views
gate20171
probability
numericalanswers
normaldistribution
+3
votes
3
answers
29
ISRO201474
What is the median of data if its mode is 15 and the mean is 30? 30 25 22.5 27.5
answered
Nov 1, 2019
in
Probability
by
kashish mittal
(
11
points)

2.7k
views
probability
statistics
meanmodemedian
isro2014
+30
votes
6
answers
30
GATE200921
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 that the ... of the following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
answered
Nov 1, 2019
in
Probability
by
Utkarsh Pathak
(
495
points)

4.3k
views
gate2009
probability
normal
+10
votes
4
answers
31
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
Oct 29, 2019
in
Probability
by
Satbir
Boss
(
23.8k
points)

1.3k
views
tifr2015
expectation
+15
votes
3
answers
32
TIFR2011A6
Assume that you are flipping a fair coin, i.e. probability of heads or tails is equal. Then the expected number of coin flips required to obtain two consecutive heads for the first time is. $4$ $3$ $6$ $10$ $5$
answered
Oct 28, 2019
in
Probability
by
Satbir
Boss
(
23.8k
points)

1.8k
views
tifr2011
probability
expectation
0
votes
0
answers
33
Gravner probability
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
asked
Oct 23, 2019
in
Probability
by
ajaysoni1924
Boss
(
10.8k
points)

90
views
gravner
probability
engineeringmathematics
+10
votes
2
answers
34
ISI2015MMA7
Suppose $X$ is distributed as Poisson with mean $λ.$ Then $E(1/(X + 1))$ is $\frac{e^{\lambda }1}{\lambda }$ $\frac{e^{\lambda }1}{\lambda +1}$ $\frac{1e^{\lambda }}{\lambda}$ $\frac{1e^{\lambda }}{\lambda + 1}$
answered
Oct 14, 2019
in
Probability
by
Gaurav Yadav
(
289
points)

878
views
isi2015
engineeringmathematics
poissondistribution
+1
vote
1
answer
35
ISI2015MMA53
The number of cars $(X)$ arriving at a service station per day follows a Poisson distribution with mean $4$. The service station can provide service to a maximum of $4$ cars per day. Then the expected number of cars that do not get service per day equals $4$ $0$ $\Sigma_{i=0}^{\infty} i P(X=i+4)$ $\Sigma_{i=4}^{\infty} i P(X=i4)$
answered
Sep 27, 2019
in
Probability
by
`JEET
Boss
(
18.9k
points)

40
views
isi2015mma
poissondistribution
expectation
+1
vote
1
answer
36
ISI2015MMA52
Two coins are tossed independently where $P$(head occurs when coin $i$ is tossed) $=p_i, \: i=1,2$. Given that at least one head has occurred, the probability that coins produced different outcomes is $\frac{2p_1p_2}{p_1+p_22p_1p_2}$ $\frac{p_1+p_22p_1p_2}{p_1+p_2p_1p_2}$ $\frac{2}{3}$ none of the above
answered
Sep 24, 2019
in
Probability
by
`JEET
Boss
(
18.9k
points)

41
views
isi2015mma
probability
independentevents
0
votes
1
answer
37
ISI2015MMA51
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n1}$ $\frac{1}{n2}$
answered
Sep 24, 2019
in
Probability
by
`JEET
Boss
(
18.9k
points)

61
views
isi2015mma
probability
randomvariable
permutationandcombination
0
votes
2
answers
38
ugc net 2018 july80
answered
Sep 23, 2019
in
Probability
by
muthuct8
(
11
points)

200
views
+1
vote
1
answer
39
ISI2018DCG6
A die is thrown thrice. If the first throw is a $4$ then the probability of getting $15$ as the sum of three throws is $\frac{1}{108}$ $\frac{1}{6}$ $\frac{1}{18}$ none of these
answered
Sep 21, 2019
in
Probability
by
`JEET
Boss
(
18.9k
points)

38
views
isi2018dcg
probability
+2
votes
1
answer
40
ISI2018DCG2
If $P$ is an integer from $1$ to $50$, what is the probability that $P(P+1)$ is divisible by $4$? $0.25$ $0.50$ $0.48$ none of these
answered
Sep 21, 2019
in
Probability
by
`JEET
Boss
(
18.9k
points)

49
views
isi2018dcg
probability
numbersystem
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