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Syllabus: Random variables, Uniform, Normal, Exponential, Poisson and Binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 0 &1&1&0&2&1&1&0&1&1&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&2&1&1&1&0&3&1&0&0&1.1&3
\\\hline\textbf{Total Marks} & 0 &5&5&2&4&3&1&6&3&1&\bf{0}&\bf{3}&\bf{6}\\\hline
\end{array}}}$$

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Recent questions in Probability

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544
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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0 votes
1 answer
545
isi_kolkata
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(E1c | E2c)? (A) 0 and 0.6 (B) 0.4 and 0.6 (C) 0.4 and 1 (D) 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(E1c | E2c)?(A) 0 and 0.6 (B) 0.4 and 0.6 (C) 0.4 and ...
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5 votes
3 answers
547
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
548
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
549
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
550
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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0 answers
552
probability
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2 votes
3 answers
553
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
555
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
2 answers
556
Made easy test
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0 votes
1 answer
558
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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560
Gate EC 2014
An unbiased coin is tossed up an infinite numbers of time.The probability that the fourth head appears at the tenth toss $.067$ $.073$ $.082$ $.091$
An unbiased coin is tossed up an infinite numbers of time.The probability that the fourth head appears at the tenth toss$.067$$.073$$.082$$.091$
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