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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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Most viewed questions in Probability

3 votes
2 answers
93
coin probability
an unbiased coin is tossed infinite no of times.The probability that 4th head appear at 10th toss is 1) 0.067 2) 0.073 3) 0.082 4) 0.091
an unbiased coin is tossed infinite no of times.The probability that 4th head appear at 10th toss is 1) 0.0672) 0.0733) 0.0824) 0.091
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3 votes
2 answers
94
probability
two independent random variables X and Y are uniformly distributed in[-1,1] probability that max(X,Y) is less than 1/2 1)3/4 2) 9/16 3)1/4 4)2/3
two independent random variables X and Y are uniformly distributed in[-1,1] probability that max(X,Y) is less than 1/21)3/42) 9/163)1/44)2/3
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2 votes
2 answers
95
UGC NET CSE | August 2016 | Part 3 | Question: 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 $99$% ? $2$ $4$ $8$ $16$
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 avai...
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4 votes
3 answers
96
random variables
Let x1 x2 x3 be three independent and identically distribuyed random variables with uniform distrbution on (0,1) find probability p(x1+x2<=x3)
Let x1 x2 x3 be three independent and identically distribuyed random variables with uniform distrbution on (0,1) find probability p(x1+x2<=x3)
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23 votes
4 answers
99
GATE CSE 1996 | Question: 2.7
The probability that top and bottom cards of a randomly shuffled deck are both aces is $\frac{4}{52} \times \frac{4}{52}$ $\frac{4}{52} \times \frac{3}{52}$ $\frac{4}{52} \times \frac{3}{51}$ $\frac{4}{52} \times \frac{4}{51}$
The probability that top and bottom cards of a randomly shuffled deck are both aces is$\frac{4}{52} \times \frac{4}{52}$$\frac{4}{52} \times \frac{3}{52}$$\frac{4}{52} \t...
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20 votes
3 answers
100
GATE CSE 1996 | Question: 1.5
Two dice are thrown simultaneously. The probability that at least one of them will have $6$ facing up is $\frac{1}{36}$ $\frac{1}{3}$ $\frac{25}{36}$ $\frac{11}{36}$
Two dice are thrown simultaneously. The probability that at least one of them will have $6$ facing up is$\frac{1}{36}$$\frac{1}{3}$$\frac{25}{36}$$\frac{11}{36}$
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5 votes
3 answers
104
ISRO2018-14
A class of $30$ students occupy a classroom containing $5$ rows of seats, with $8$ seats in each row. If the students seat themselves at random, the probability that sixth seat in the fifth row will be empty is: $1/5$ $1/3$ $1/4$ $2/5$
A class of $30$ students occupy a classroom containing $5$ rows of seats, with $8$ seats in each row. If the students seat themselves at random, the probability that sixt...
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2 votes
5 answers
105
expectation
A fair coin is tossed repeatedly till both head and tail appear atleast once. Average no of tosses required is ?
A fair coin is tossed repeatedly till both head and tail appear atleast once. Average no of tosses required is ?
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4 votes
3 answers
106
ISRO2014-74
What is the median of data if its mode is $15$ and the mean is $30?$ $30$ $25$ $22.5$ $27.5$
What is the median of data if its mode is $15$ and the mean is $30?$$30$$25$$22.5$$27.5$
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25 votes
2 answers
109
GATE CSE 1994 | Question: 2.8
Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is _______
Let $A, B,$ and $C$ be independent events which occur with probabilities $0.8, 0.5,$ and $0.3$ respectively. The probability of occurrence of at least one of the event is...
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