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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

2 votes
1 answer
721
counting
Number of words of 4 letters that can be formed with the letters of the word IITJEE is 42 256 102 142
Number of words of 4 letters that can be formed with the letters of the word IITJEE is42256102142
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13 votes
2 answers
722
ISI2015-MMA-7
Suppose $X$ is distributed as Poisson with mean $λ.$ Then $E(1/(X + 1))$ is $\frac{e^{\lambda }-1}{\lambda }$ $\frac{e^{\lambda }-1}{\lambda +1}$ $\frac{1-e^{-\lambda }}{\lambda}$ $\frac{1-e^{-\lambda }}{\lambda + 1}$
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{1-e^{-\lambda }}{\l...
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3 votes
2 answers
723
#probability
8 pairs of shoes are in a closet. 8 shoes are selected at random. The probability that there will be at least one pair and at most 3 pairs amongst selected shoes are?
8 pairs of shoes are in a closet. 8 shoes are selected at random. The probability that there will be at least one pair and at most 3 pairs amongst selected shoes are?
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1 votes
1 answer
726
Probability
in a game of bridge the entire deck of 52 cards is dealt out to 4 players.What is the probability that i)one of the players receive all 13 spades ii )each player receives one ace?
in a game of bridge the entire deck of 52 cards is dealt out to 4 players.What is the probability that i)one of the players receive all 13 spadesii )each player receives...
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1 votes
0 answers
728
Explanation needed!!
You roll a fair four-sided die. If the result is 1 or 2, you roll once more but otherwise, you stop. What is the probability that the sum total of your rolls is at least 4? 9/8 9/16 3/5 1/16
You roll a fair four-sided die. If the result is 1 or 2, you roll oncemore but otherwise, you stop. What is the probability that the sum total of yourrolls is at least 4?...
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1 votes
1 answer
730
Ravi asked his neighbor to water a delicate plant while he is away.
Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability $4/5$ and with water, it would die with probability $3/20$ ... forgot to water the plant? (A) $4/5$ (B) $27/43$ (C) $16/43$ (D) $2/25$
Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability $4/5$ and with water, it would die with probabilit...
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1 votes
2 answers
731
The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3
The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3 . If each fires once and the target is hit only once, what is the probability that A hits the target?
The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3 . If each fires once and the target is hit only once, what is the probabilit...
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0 votes
1 answer
732
probability
If from each box of the three boxes containing $3$ white and $3$ black,$2$ white and $2$ black,$1$ white and $3$ black,one ball is drawn at random ,then the probability that $2$ white and $1$ black ball will be drawn ?
If from each box of the three boxes containing $3$ white and $3$ black,$2$ white and $2$ black,$1$ white and $3$ black,one ball is drawn at random ,then the probability t...
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2 votes
1 answer
733
probability
There are $N$ persons sitting in a row. Two of them are selected at random.The probability that two selected persons are not together ?
There are $N$ persons sitting in a row. Two of them are selected at random.The probability that two selected persons are not together ?
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1 votes
2 answers
734
probability
There are four machines and it is known that exactly two of them are faulty .They are tested one by one in a random order till both the faulty machines are identified ,then the probability that only two tests are needed ?
There are four machines and it is known that exactly two of them are faulty .They are tested one by one in a random order till both the faulty machines are identified ,th...
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0 votes
1 answer
735
MEBook
Assume that a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time.So find the probability that the aggregate of total of values that turn up is at least 6?
Assume that a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time.So find the probability that the aggregate of t...
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0 votes
1 answer
736
probability
A man takes a step forward with probability 0.4 and backwards with probability 0.6 .find the probability that at the end of eleven steps he is just one step away from the starting point
A man takes a step forward with probability 0.4 and backwards with probability 0.6 .find the probability that at the end of eleven steps he is just one step away from the...
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1 votes
2 answers
737
ISRO 2014- probability [EE]
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is (A) 140 (B) 196 (C) 280 (D) 346
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him ...
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1 votes
1 answer
738
ISRO 2013- probability [EE]
Ten percent of screws produced in a certain factory turn out to be defective. Find the probability that in a sample of 10 screws chosen at random, exactly two will be defective. a) 0.2 b) 0.25 c) 0.8 d) 0.3 79.
Ten percent of screws produced in a certain factory turn out to be defective. Find the probability that in a sample of 10 screws chosen at random, exactly two will be def...
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0 votes
2 answers
739
ISRO 2013 Probability [EE]
An urn contains 5 black and 5 white balls. The probability of drawing two balls of the same colour a) 2/9 b) 4/9 c) 1/9 d) 5/9
An urn contains 5 black and 5 white balls. The probability of drawing two balls of the same coloura) 2/9b) 4/9c) 1/9d) 5/9
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0 votes
1 answer
740
ISRO 2013- Probability/Leap year [Mech]
Chance that a leap year selected at random will contain 53 Sundays is (a) 3/7 (b) 7/2 (c) 7/3 (d) 2/7
Chance that a leap year selected at random will contain 53 Sundays is(a) 3/7(b) 7/2(c) 7/3(d) 2/7
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