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Recent questions and answers in Probability
0
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1
answer
1
ESE 2018
In a sample of 100 students, the mean of the marks (only integers) obtained by them in a test is 14 with its standard deviation of 2.5(marks obtained can be fitted with a normal distribution ).the percentage of students scoring 16 marks is a)36 b)23 c)12 d)10 (Area under standard normal curve between z=0 and z=0.6 is 0.2257 ; and between z=0 and z=1.0 is 0.3413)
answered
Jul 2
in
Probability
by
mohan123

442
views
probability
+1
vote
3
answers
2
ProbabilityGFG
In a bunch of $13$ Tshirts only $1$ is of Medium size, which is correct fit for the searching person. Each time wrong size is picked, the person throws it away and pick the next Tshirt. What is the probability that the correct size Tshirt can be searched in $8^{th}$ attempt ? My attempt : $\frac{1}{13}$ where i went wrong ?
answered
Jun 17
in
Probability
by
Jhaiyam

470
views
probability
+10
votes
4
answers
3
GATE19952.14
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: $\frac{2}{3}$ $\frac{4}{5}$ $\frac{1}{2}$ $\frac{1}{3}$
answered
Jun 17
in
Probability
by
manikantsharma

3.3k
views
gate1995
probability
normal
+1
vote
1
answer
4
ISI2017MMA8
Let $X_1$, and $X_2$ and $X_3$ be chosen independently from the set $\{0, 1, 2, 3, 4\}$, each value being equally likely. What is the probability that the arithmetic mean of $X_1, X_2$ and $X_3$ is the same as their geometric mean? $\frac{1}{5^2}\\$ $\frac{1}{5^3}\\$ $\frac{3!}{5^3}\\$ $\frac{3}{5^3}$
answered
Jun 7
in
Probability
by
Amartya

160
views
isi2017mma
engineeringmathematics
probability
+20
votes
4
answers
5
GATE2014248
The probability that a given positive integer lying between $1$ and $100$ (both inclusive) is NOT divisible by $2$, $3$ or $5$ is ______ .
answered
Jun 6
in
Probability
by
luc_Bloodstone

3k
views
gate20142
probability
numericalanswers
normal
0
votes
2
answers
6
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
Jun 5
in
Probability
by
smsubham

126
views
isi2016mmamma
probability
randomvariable
poissondistribution
expectation
0
votes
1
answer
7
Probability Gravner 75.a
What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?
answered
Jun 4
in
Probability
by
smsubham

84
views
gravner
probability
engineeringmathematics
randomvariable
normaldistribution
+6
votes
2
answers
8
TIFR2010A10
A drawer contains $2$ Blue, $4$ Red and $2$ Yellow balls. No two balls have the same radius. If two balls are randomly selected from the drawer, what is the probability that they will be of the same colour? $\left(\dfrac{2}{7}\right)$ $\left(\dfrac{2}{5}\right)$ $\left(\dfrac{3}{7}\right)$ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{3}{5}\right)$
answered
May 31
in
Probability
by
vipin.gautam1906

646
views
tifr2010
probability
+15
votes
6
answers
9
GATE201815
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 trial ... probable and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
answered
May 31
in
Probability
by
vipin.gautam1906

4.1k
views
gate2018
probability
normal
numericalanswers
+19
votes
3
answers
10
TIFR2011A9
You have to play three games with opponents $A$ and $B$ in a specified sequence. You win the series if you win two consecutive games. $A$ is a stronger player than $B$. Which sequence maximizes your chance of winning the series? $AAB$ $ABA$ $BAB$ $BAA$ All are the same.
answered
May 28
in
Probability
by
Joyoshish Saha

802
views
tifr2011
probability
+1
vote
3
answers
11
probability
Let x be the number obtained from rolling a fair dice and you toss an unbiassed coin X times. What is the probablity that X=5 given that you have obtained 3 heads from X tosses?
answered
May 18
in
Probability
by
DIBAKAR MAJEE

339
views
conditionalprobability
0
votes
2
answers
12
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
May 3
in
Probability
by
DIBAKAR MAJEE

152
views
tifr2020
engineeringmathematics
probability
+6
votes
3
answers
13
Probability Gate EE 2016
Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is _________.
answered
Apr 13
in
Probability
by
ragnarok

2.9k
views
probability
engineeringmathematics
+1
vote
1
answer
14
NIELIT 2017 July Scientist B (IT)  Section B: 23
The probability that top and bottom cards of a randomly shuffled deck are both aces is: $4/52\times 4/52$ $4/52\times 3/52$ $4/52\times 3/51$ $4/52\times 4/51$
answered
Apr 3
in
Probability
by
immanujs

70
views
nielit2017julyscientistbit
+11
votes
5
answers
15
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
Apr 1
in
Probability
by
tanishk1999

1.6k
views
tifr2015
expectation
0
votes
1
answer
16
NIELIT 2016 MAR Scientist B  Section B: 16
A box contains $10$ screws, $3$ of which are defective. Two screws are drawn at random with replacement. The probability that none of two screws is defective will be $100\%$ $50\%$ $49\%$ None of these.
answered
Apr 1
in
Probability
by
haralk10

74
views
nielit2016marscientistb
+1
vote
1
answer
17
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
Mar 29
in
Probability
by
haralk10

89
views
ugcnetdec2007ii
0
votes
1
answer
18
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 20
in
Probability
by
SatyamK

63
views
isi2016mmamma
probability
independentevents
+1
vote
2
answers
19
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

416
views
0
votes
2
answers
20
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

266
views
isi2018mma
engineeringmathematics
probability
0
votes
1
answer
21
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
by
ankitgupta.1729

79
views
tifr2020
+5
votes
4
answers
22
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 27
in
Probability
by
immanujs

1.5k
views
gate2020cs
numericalanswers
probability
0
votes
1
answer
23
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 winners ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
answered
Feb 26
in
Probability
by
ankitgupta.1729

112
views
tifr2020
engineeringmathematics
probability
independentevents
0
votes
1
answer
24
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

97
views
tifr2020
engineeringmathematics
probability
expectation
0
votes
0
answers
25
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 11
in
Probability
by
Lakshman Patel RJIT

60
views
tifr2020
engineeringmathematics
probability
uniformdistribution
+2
votes
2
answers
26
UGCNETAUG2016III: 54
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

1.8k
views
ugcnetaug2016iii
probability
+20
votes
4
answers
27
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
by
Kushagra गुप्ता

4.5k
views
gate20142
probability
numericalanswers
normal
0
votes
1
answer
28
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 14
in
Probability
by
Tuhin Dutta

375
views
isro2020
probability
standarddeviation
normal
+31
votes
4
answers
29
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

3.9k
views
gate20153
probability
randomvariable
normal
numericalanswers
+26
votes
5
answers
30
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 12
in
Probability
by
arjuno

4.3k
views
gate2011
probability
normal
+26
votes
8
answers
31
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

5.5k
views
gate2007
probability
easy
uniformdistribution
+16
votes
5
answers
32
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 10
in
Probability
by
JashanArora

2.6k
views
gate2008
probability
normal
+7
votes
5
answers
33
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

605
views
cmi2012
probability
+16
votes
6
answers
34
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

1.2k
views
tifr2010
probability
binomialdistribution
+2
votes
1
answer
35
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 8
in
Probability
by
Dharmendra Tiwari

255
views
go2019flt1
statistics
probability
+6
votes
4
answers
36
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

4.2k
views
probability
isro2014
+2
votes
1
answer
37
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

186
views
conditionalprobability
+5
votes
4
answers
38
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

1.5k
views
gate2019
probability
0
votes
1
answer
39
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

128
views
+6
votes
5
answers
40
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

802
views
tifr2012
probability
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