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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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probabiltiy
5 integers randomly chosen from 1 to 2015. What is the probability that there is a pair of integers whose difference is a multiple of 4?
5 integers randomly chosen from 1 to 2015. What is the probability that there is a pair of integers whose difference is a multiple of 4?
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A player in the Powerball lottery picks five different integers between 1 and 59, inclusive, and a sixth integer between 1 and 39
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It is known that a bus will arrive at random at a certain location sometime between 3:00 P.M. and 3:30 P.M.
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GATE IT 2005 | Question: 32
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is $3$ $4$ $5$ $6$
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GATE CSE 2001 | Question: 2.4
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day? $\dfrac{1}{7^7}\\$ $\dfrac{1}{7^6}\\$ $\dfrac{1}{2^7}\\$ $\dfrac{7}{2^7}\\$
Seven (distinct) car accidents occurred in a week. What is the probability that they all occurred on the same day?$\dfrac{1}{7^7}\\$$\dfrac{1}{7^6}\\$$\dfrac{1}{2^7}\\$$\...
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