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Recent questions tagged probability

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752
Probability
Prove for a positive integer valued random variable, $X$ , and for positive integers $a < b$ \begin{align*} &P(X \geq b) \leq \left [ \left ( \frac{E(X)}{b} \right ) - P(a \leq X < b)\cdot \left ( \frac{a}{b} \right ) \right ] \\ \end{align*}
Prove for a positive integer valued random variable, $X$ , and for positive integers $a < b$\begin{align*} &P(X \geq b) \leq \left [ \left ( \frac{E(X)}{b} \right ) - P(...
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5 votes
3 answers
754
ISRO2018-14
A class of $30$ students occupy a classroom containing $5$ rows of seats, with $8$ seats in each row. If the students seat themselves at random, the probability that sixth seat in the fifth row will be empty is: $1/5$ $1/3$ $1/4$ $2/5$
A class of $30$ students occupy a classroom containing $5$ rows of seats, with $8$ seats in each row. If the students seat themselves at random, the probability that sixt...
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0 votes
2 answers
755
Maths: Probability Distribution
Suppose X is a uniform random variable between 0.50 and 1.00. What is the probability that a randomly selected value of X is between 0.55 and 0.60 or between 0.75 and 0.85? A. 0.00 B. 0.15 C. 0.60 D. 0.30
Suppose X is a uniform random variable between 0.50 and 1.00. What is the probability that a randomly selected value of X is between 0.55 and 0.60 or between 0.75 and 0.8...
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3 votes
2 answers
756
PGEE 2018
Three person plays a game by tossing a coin, if atleast one of the outcome is different from another end is declared, coins are biased with probability of head is 1/4 what is probability that game ends in first round
Three person plays a game by tossing a coin, if atleast one of the outcome is different from another end is declared, coins are biased with probability of head is 1/4 wha...
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2 votes
2 answers
757
PGEE 2018
4 person wearing different hat went to restaurant, they gave there hat to manager, manager has habit of forgetting thing while returning manager gave hat back to each person, probability that none of the person gets there respective hats is ?
4 person wearing different hat went to restaurant, they gave there hat to manager, manager has habit of forgetting thing while returning manager gave hat back to each per...
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2 votes
3 answers
760
Probability Practice
Six balls are to be randomly chosen from an urn containing 8 red, 10 green, and 12 blue balls. What is the probability at least one red ball, one blue and one green ball is chosen?
Six balls are to be randomly chosen from an urn containing 8 red, 10 green, and 12 blue balls.What is the probability at least one red ball, one blue and one green ball i...
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0 votes
1 answer
762
B. S. Grewal Engineering Mathematics- Probability
A student has to answer $9$ out of $12$ questions. How many ways if he has to answer at least $4$ out of first $5$ questions?
A student has to answer $9$ out of $12$ questions. How many ways if he has to answer at least $4$ out of first $5$ questions?
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0 votes
1 answer
764
probability
From a pack of $52$ cards, all the face cards are removed and four cards are drawn. Then the probability that they are of different suit and different denomination is
From a pack of $52$ cards, all the face cards are removed and four cards are drawn. Then the probability that they are of different suit and different denomination is
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1 votes
1 answer
766
Gate probability
Two players,$A$ and $B$,alternately keep rolling a fare dice.The person to get six first wins the game.Given that player $A$ starts the game,the probability that $A$ wins the game is $5/11$ $1/2$ $7/13$ $6/11$
Two players,$A$ and $B$,alternately keep rolling a fare dice.The person to get six first wins the game.Given that player $A$ starts the game,the probability that $A$ wins...
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0 votes
1 answer
767
Gate PI 2012
A fair coin is tossed till a head appears for the first time.The probability that the number of required tossed is odd,is $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$
A fair coin is tossed till a head appears for the first time.The probability that the number of required tossed is odd,is$\left(\dfrac{1}{3}\right)$$\left(\dfrac{1}{2}\ri...
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2 votes
2 answers
768
Gate probability
A party of n persons take their seats at random at a round table,then the probability that two specified person do not sit together is $\left(\dfrac{2}{n-1}\right)$ $\left(\dfrac{n-3}{n-1}\right)$ $\left(\dfrac{n-2}{n-1}\right)$ $\left(\dfrac{1}{n-1}\right)$
A party of n persons take their seats at random at a round table,then the probability that two specified person do not sit together is$\left(\dfrac{2}{n-1}\right)$$\left(...
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0 votes
2 answers
773
ISI-2014-2
Two integers $m$ and $n$ are chosen at random with replacement from the natural numbers $1,2,.....9$. The probability that $m^2-n^2$ is divisible by $4$ is $\dfrac{41}{81}$ $\dfrac{37}{81}$ $\dfrac{2}{3}$ $\dfrac{4}{9}$
Two integers $m$ and $n$ are chosen at random with replacement from the natural numbers $1,2,.....9$. The probability that $m^2-n^2$ is divisible by $4$ is$\dfrac{41}{81}...
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2 votes
3 answers
774
ISI-2014-11
Let $X_1,X_2,X_3,X_4$ be i.i.d. random variables each assuming the value $1$ and $-1$ with probability $\dfrac{1}{2}$ each. Then, the probability that the matrix $\begin{pmatrix}X_1 &X_2\\ X_3 &X_4\end{pmatrix}$ is nonsingular equals $1/2$ $3/8$ $5/8$ $1/4$
Let $X_1,X_2,X_3,X_4$ be i.i.d. random variables each assuming the value $1$ and $-1$ with probability $\dfrac{1}{2}$ each. Then, the probability that the matrix $\begin{...
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1 votes
0 answers
775
ISI 2014-10
$E1$ and $E2$ are two events such that $P(E1) = 0.2$ and $P(E2) = 0.5$. What are the minimum and maximum possible values of $P(\dfrac{\text{complement of (E1)}}{\text{complement of (E2)}})$? $\text{0 and 0.6}$ $\text{0.4 and 0.6}$ $\text{0.4 and 1}$ $\text{0.6 and 1}$
$E1$ and $E2$ are two events such that $P(E1) = 0.2$ and $P(E2) = 0.5$.What are the minimum and maximum possible values of $P(\dfrac{\text{complement of (E1)}}{\text{comp...
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0 votes
1 answer
776
#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?
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 ...
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2 votes
1 answer
779
Birthday Paradox
There are 60 persons in a room.We have choosen 10 person at random. What is the probability that exactly 2 person among them have same birthday?
There are 60 persons in a room.We have choosen 10 person at random. What is the probability that exactly 2 person among them have same birthday?
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