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Recent questions and answers in Probability
+4
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5
answers
1
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
3 days
ago
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tifr2012
probability
0
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1
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2
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
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Probability
by
Mk Utkarsh
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probability
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0
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1
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3
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
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Probability
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Mk Utkarsh
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probability
gravner
engineeringmathematics
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0
votes
1
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4
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
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probability
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0
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1
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5
Probability  Gravner69.a
$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$ (a) Determine $c$.
answered
Nov 27
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Probability
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16
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gravner
probability
engineeringmathematics
randomvariable
+20
votes
4
answers
6
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
in
Probability
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gate2006it
probability
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+1
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3
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7
ISI2017DCG23
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability of choosing a nonzero determinant is $\frac{3}{16}$ $\frac{3}{8}$ $\frac{1}{4}$ none of these
answered
Nov 19
in
Probability
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isi2017dcg
probability
randomvariable
determinants
0
votes
2
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8
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
in
Probability
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Yash4444
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29
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isi2017dcg
probability
ballsinbins
+1
vote
0
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9
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
in
Probability
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Ayush Upadhyaya
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probability
+12
votes
5
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10
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
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Probability
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commenter commenter
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tifr2013
probability
+13
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4
answers
11
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
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Probability
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gate1994
probability
normal
descriptive
conditionalprobability
+5
votes
4
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12
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
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Probability
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tifr2013
probability
+16
votes
7
answers
13
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
in
Probability
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Utkarsh Pathak
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gate2005
probability
binomialdistribution
easy
+2
votes
2
answers
14
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? $\frac{1}{12}$ $\frac{1}{6}$ $\frac{2}{9}$ $\frac{2}{7}$
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Nov 3
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Probability
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cmi2019
probability
fairdie
faircoin
+21
votes
4
answers
15
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 ______________ .
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Nov 2
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Probability
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gate20171
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+3
votes
3
answers
16
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
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Probability
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kashish mittal
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meanmodemedian
isro2014
+28
votes
6
answers
17
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
in
Probability
by
Utkarsh Pathak
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405
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3.9k
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gate2009
probability
normal
+10
votes
4
answers
18
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
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Probability
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tifr2015
expectation
+14
votes
3
answers
19
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
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Probability
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Satbir
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tifr2011
probability
expectation
0
votes
0
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20
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
in
Probability
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ajaysoni1924
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gravner
probability
engineeringmathematics
+10
votes
2
answers
21
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
in
Probability
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Gaurav Yadav
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isi2015
engineeringmathematics
poissondistribution
0
votes
1
answer
22
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
in
Probability
by
`JEET
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9
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isi2015mma
poissondistribution
expectation
0
votes
1
answer
23
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
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Probability
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17
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isi2015mma
probability
independentevents
0
votes
1
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24
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 $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n1}$ $\frac{1}{n2}$
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Sep 24
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Probability
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isi2015mma
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permutationandcombination
0
votes
2
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25
ugc net 2018 july80
answered
Sep 23
in
Probability
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192
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+1
vote
1
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26
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
in
Probability
by
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20
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isi2018dcg
probability
dice
+2
votes
1
answer
27
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
in
Probability
by
`JEET
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13.1k
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23
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isi2018dcg
probability
numbersystem
+1
vote
1
answer
28
ISI2017DCG22
Let $A_1,A_2,A_3, \dots , A_n$ be $n$ independent events such that $P(A_i) = \frac{1}{i+1}$ for $i=1,2,3, \dots , n$. The probability that none of $A_1, A_2, A_3, \dots , A_n$ occurs is $\frac{n}{n+1}$ $\frac{1}{n+1}$ $\frac{n1}{n+1}$ none of these
answered
Sep 20
in
Probability
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Ashwani Kumar 2
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18
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isi2017dcg
probability
independentevents
+1
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1
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29
CMI2018A7
Let $C_{n}$ be the number of strings $w$ consisting of $n$ $X's$ and $n$ $Y's$ such that no initial segment of $w$ has more $Y's$ than $X's.$ Now consider the following problem. A person stands on the edge of a swimming pool holding a bag of $n$ red and $n$ blue balls. He draws a ... $\frac{C_{n}}{\binom{2n}{n}}$ $\frac{n\cdot C_{n}}{(2n)!}$ $\frac{n\cdot C_{n}}{\binom{2n}{n}}$
answered
Sep 14
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Probability
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cmi2018
conditionalprobability
ballsinbins
+1
vote
1
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30
CMI2018A8
There are $7$ switches on a switchboard, some of which are on and some of which are off. In one move, you pick any $2$ switches and toggle each of themif the switch you pick is currently off, you turn it on, if it is on, you turn it off. Your aim is to execute a sequence of ... (off,on,off,on,off,off,on) (off,on,on,on,on,on,off) (on,off,on,on,on,on,on) (off,off,off,off,off,on,off)
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Sep 13
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cmi2018
conditionalprobability
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31
CMI2018A6
You are given two coins $A$ and $B$ that look identical. The probability that coin $A$ turns up heads is $\frac{1}{4}$, while the probability that coin $B$ turns up heads is $\frac{3}{4}.$ You choose one of the coins at random and toss it twice. If both the outcomes are heads, what is the probability that you chose coin $B?$ $\frac{1}{16}$ $\frac{1}{2}$ $\frac{9}{16}$ $\frac{9}{10}$
answered
Sep 13
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Probability
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Satbir
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cmi2018
conditionalprobability
cointoss
0
votes
1
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32
Sheldon Ross Chapter2 Question15b
If it is assumed that all $\binom{52}{5}$ poker hands are equally likely, what is the probability of being dealt two pairs? (This occurs when the cards have denominations a, a, b, b, c, where a, b, and c are all distinct.) my approach is: selecting a ... I'm getting answer 0.095 but in the book answer is given 0.0475 where am I going wrong?
answered
Sep 11
in
Probability
by
Kvothe
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101
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125
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probability
sheldonross
engineeringmathematics
+13
votes
6
answers
33
GATE19981.1
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is $\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}$
answered
Sep 7
in
Probability
by
gateuser123
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21
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2.4k
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gate1998
probability
easy
+17
votes
7
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34
GATE20033
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
answered
Aug 28
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gate2003
probability
easy
conditionalprobability
0
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1
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35
#Normal distribution
If a certain normal distribution of $X$, the probability is $0.5$ that $X$ is less than $500$ and $0.0227$ that $X$ is greater than $650$. What is the standard deviation of $X$? How to compute S.D, of above?
answered
Aug 24
in
Probability
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GoalSet1
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203
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90
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probability
+12
votes
4
answers
36
TIFR2012A20
There are $1000$ balls in a bag, of which $900$ are black and $100$ are white. I randomly draw $100$ balls from the bag. What is the probability that the $101$st ball will be black? $9/10$ More than $9/10$ but less than $1$. Less than $9/10$ but more than $0$. $0$ $1$
answered
Aug 16
in
Probability
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tifr2012
probability
0
votes
1
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37
Probability  Gravner49.c
You have $16$ balls, $4$ green, and $9$ red. You also have $3$ urns. For each of the $16$ balls. you select an urn at random and put the ball into it.(Urns are large enough to accommodate any number of balls.) (c) What is the probability that each urn contains all three colors?
answered
Jul 31
in
Probability
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blackcloud
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257
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27
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gravner
probability
engineeringmathematics
+13
votes
13
answers
38
TIFR2012A1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What probability should Anthony ... $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above
answered
Jul 25
in
Probability
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tifr2012
probability
conditionalprobability
+1
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3
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39
Suppose that 100 people enter a contest and that different winners are selected at random for first, second, and third prizes. What is the probability that Michelle wins one of these prizes if she is one of the contestants?
answered
Jul 21
in
Probability
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0
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40
Probability
Suppose that a bag contains 8 blue cubes and 4 green cubes. We draw 2 cubes from the bag without replacement. It is given that blue balls are of weight 1Kg and green balls are of weight 0.5 Kg. Suppose that the probability that a given cube in the bag ... is its weight divided by the sum of the weights of all cubes currently in the bag. What is the probability that both cubes are blue.
answered
Jul 20
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Probability
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63
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52
views
probability
engineeringmathematics
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