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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 answered questions in Probability

61 votes
3 answers
151
GATE CSE 2014 Set 1 | Question: 2
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ .
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24 votes
3 answers
152
GATE CSE 2005 | Question: 12, ISRO2009-64
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is : $f(b-a)$ $f(b) - f(a)$ $\int\limits_a^b f(x) dx$ $\int\limits_a^b xf (x)dx$
Let $f(x)$ be the continuous probability density function of a random variable $x$, the probability that $a < x \leq b$, is :$f(b-a)$$f(b) - f(a)$$\int\limits_a^b f(x) dx...
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56 votes
3 answers
153
GATE CSE 2010 | Question: 27
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$?$\left(\dfrac{1}{625}\right)$$\left(\dfrac{4}{625}\right)$$\left(\dfrac{12}{625}\right)$$\lef...
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16 votes
3 answers
154
GATE CSE 2004 | Question: 25
If a fair coin is tossed four times. What is the probability that two heads and two tails will result? $\frac{3}{8}$ $\frac{1}{2}$ $\frac{5}{8}$ $\frac{3}{4}$
If a fair coin is tossed four times. What is the probability that two heads and two tails will result?$\frac{3}{8}$$\frac{1}{2}$$\frac{5}{8}$$\frac{3}{4}$
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2 votes
2 answers
158
GATE CSE 2024 | Set 1 | Question: 53
A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to $3$ decimal places) that both balls drawn are red is ___________.
A bag contains $10$ red balls and $15$ blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off ...
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14 votes
2 answers
165
GO Classes 2024 | Weekly Quiz 8 | Conditional Probability | Question: 4
$A$ and $B$ are two events. If $P(A, B)$ decreases while $P(A)$ increases, what must be true: $P(A \mid B)$ decreases $P(B \mid A)$ decreases $P(B)$ decreases All of above
$A$ and $B$ are two events. If $P(A, B)$ decreases while $P(A)$ increases, what must be true:$P(A \mid B)$ decreases$P(B \mid A)$ decreases$P(B)$ decreasesAll of above
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