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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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Highest voted questions in Probability

1 votes
1 answer
482
ISI2017-DCG-22
Let $A_1,A_2,A_3, \dots , A_n$ be $n$ independent events such that $P(A_i) = \frac{1}{i+1}$ for $i=1,2,3, \dots , n$. The probability that none of $A_1, A_2, A_3, \dots , A_n$ occurs is $\frac{n}{n+1}$ $\frac{1}{n+1}$ $\frac{n-1}{n+1}$ none of these
Let $A_1,A_2,A_3, \dots , A_n$ be $n$ independent events such that $P(A_i) = \frac{1}{i+1}$ for $i=1,2,3, \dots , n$. The probability that none of $A_1, A_2, A_3, \dots ,...
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1 votes
2 answers
485
Gate 2018: Probability
In a box, there are $2$ red, $3$ black and $4$ blue coloured balls. The probability of drawing $2$ blue balls in sequence without replacing, and then drawing $1$ black ball from this box is _________ %.
In a box, there are $2$ red, $3$ black and $4$ blue coloured balls. The probability of drawing $2$ blue balls in sequence without replacing, and then drawing $1$ black ba...
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1 votes
0 answers
486
Probability density function
Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf f(r) = 2e^(−2r) on [0, ∞). Find the pdf of the waiting time per customer T = 1/R.
Let R be the rate at which customers are served in a queue. Suppose that R isexponential with pdf f(r) = 2e^(−2r) on [0, ∞).Find the pdf of the waiting time per custo...
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1 votes
1 answer
488
JEST Sample Question 1-c
If a fair die (with 6 faces) is cast twice, what is the probability that the two numbers obtained differ by 2? (A) 1/12 (B) 1/6 (C) 2/9 (D) 1/2
If a fair die (with 6 faces) is cast twice, what is the probability that the twonumbers obtained differ by 2?(A) 1/12(B) 1/6(C) 2/9(D) 1/2
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1 votes
1 answer
490
A family has two children. Given that one of the children is a boy, what is the probability that both children are boys?
I was doing this question using conditional probability formula.... i.e P(2/1)=? Probability of 2nd child to be boy given that 1st child is a boy. By formula, P(2/1)=P(2,...
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1 votes
1 answer
493
Applied Course | Mock GATE | Test 1 | Question: 33
Person "A" says the truth $60 \%$ of the time, and person "B" does so $90 \%$ of the time. In what percentage of cases are they likely to contradict each other in stating the same fact? $6 \%$ $36 \%$ $42 \%$ $54 \%$
Person "A" says the truth $60 \%$ of the time, and person "B" does so $90 \%$ of the time. In what percentage of cases are they likely to contradict each other in stating...
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1 votes
0 answers
494
Self Doubt
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1 votes
1 answer
495
Probability
Suppose we want to pick two numbers from {1,2……,100} randomly . The probability that sum of the two numbers is divisible by 5 is _________________
Suppose we want to pick two numbers from {1,2……,100} randomly . The probability that sum of the two numbers is divisible by 5 is _________________
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1 votes
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496
MadeEasy Test Series: Probabilty - Probability
The probability of a man hitting a target in one fire is 1/6. The number of times at least he must fire at the target in order that his chance of hitting the target at least once will exceed 2/5 will be ?
The probability of a man hitting a target in one fire is 1/6. The number of times at least he must fire at the target in order that his chance of hitting the target at le...
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1 votes
0 answers
497
Random Variable
Let X and Y are two random variables with E(X)=10,E(Y)=20 and Var(X)=25,Var(Y)=36 and E(X.Y)=225. Now consider Z=aX-bY+1. Find a and b when E(Z)=1 and Var(Z)=1.
Let X and Y are two random variables with E(X)=10,E(Y)=20 and Var(X)=25,Var(Y)=36 and E(X.Y)=225.Now consider Z=aX-bY+1.Find a and b when E(Z)=1 and Var(Z)=1.
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1 votes
1 answer
500
Probability question (Bayes theorem)
If H occurs, select number from 1 to 10. If T occurs, select number from 11 to 30. If selected number is prime, find the probability that it is in H.
If H occurs, select number from 1 to 10. If T occurs, select number from 11 to 30. If selected number is prime, find the probability that it is in H.
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