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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

8 votes
5 answers
33
CMI2012-A-07
A man has three cats. At least one is male. What is the probability that all three are male? $\frac{1}{2}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{3}{8}$
A man has three cats. At least one is male. What is the probability that all three are male?$\frac{1}{2}$$\frac{1}{7}$$\frac{1}{8}$$\frac{3}{8}$
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2 votes
5 answers
34
expectation
A fair coin is tossed repeatedly till both head and tail appear atleast once. Average no of tosses required is ?
A fair coin is tossed repeatedly till both head and tail appear atleast once. Average no of tosses required is ?
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18 votes
5 answers
38
TIFR CSE 2013 | Part A | Question: 14
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is $\dfrac{1}{(2n)}$ $\dfrac{1}{[(6n)!]}$ $1 - 6^{-n}$ $6^{-n}$ None of the above
An unbiased die is thrown $n$ times. The probability that the product of numbers would be even is$\dfrac{1}{(2n)}$$\dfrac{1}{[(6n)!]}$$1 - 6^{-n}$$6^{-n}$None of the abov...
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2 votes
5 answers
40
question on probability
Two aeroplanes I and II bomb a target in succession. The probability of I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if the first misses the target.The probability that the target is hit by the second plane ?
Two aeroplanes I and II bomb a target in succession. The probability of I and II scoring a hit correctly are 0.3 and 0.2 respectively. The second plane will bomb only if...
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34 votes
5 answers
41
GATE IT 2008 | Question: 23
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday? $1-\dfrac{365-364 \dots (365-r+1)}{365^{r}}$ ... $\dfrac{365 \cdot 364 \dots (365-r+1)}{365^{r}}$
What is the probability that in a randomly chosen group of $r$ people at least three people have the same birthday?$1-\dfrac{365-364 \dots (365-r+1)}{365^{r}}$$\dfrac{365...
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35 votes
5 answers
42
GATE CSE 2014 Set 3 | Question: 48
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of $P(A)P(B)$ is_____.
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of ...
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39 votes
5 answers
43
GATE CSE 2014 Set 1 | Question: 48
Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $\dfrac{X}{1296}$. The value of $X$ is _______
Four fair six-sided dice are rolled. The probability that the sum of the results being $22$ is $\dfrac{X}{1296}$. The value of $X$ is _______
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42 votes
5 answers
46
GATE CSE 2003 | Question: 60, ISRO2007-45
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ ... $\int_0^t f_1(x)f_2(t-x)dx$ $\max\{f_1(t),f_2(t)\}$
A program consists of two modules executed sequentially. Let $f_1(t)$ and $f_2(t)$ respectively denote the probability density functions of time taken to execute the two ...
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22 votes
5 answers
47
GATE CSE 2002 | Question: 2.16
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is $\frac{1}{16}$ $\frac{1}{8}$ $\frac{7}{8}$ $\frac{15}{16}$
Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is$\frac{1}{16}$$\frac{1}{8}$$\frac{7}{8}$$\frac{15}{16}$
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14 votes
5 answers
48
GATE CSE 1995 | Question: 1.18
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$ $\left(\dfrac{9}{10}\right)^{3}$ $\dfrac{27}{75}$ $\dfrac{18}{25}$
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$$\left(\dfrac{9}{10}\right)^...
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