Syllabus: Random variables, Uniform, Normal, Exponential, Poisson and Binomial distributions. Mean, median, mode and standard deviation. Conditional probability and Bayes theorem

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 0 &1&1&0&2&1&1&0&1&1&0&0.8&2
\\\hline\textbf{2 Marks Count} & 0 &2&2&1&1&1&0&3&1&0&0&1.1&3
\\\hline\textbf{Total Marks} & 0 &5&5&2&4&3&1&6&3&1&\bf{0}&\bf{3}&\bf{6}\\\hline
\end{array}}}$$

Recent questions in Probability

5 votes

1 answer

811

Probability
In a boxing tournament 2n equally skilled players P1,P2,P3...........P$2^{n}$ ... $\frac{3}{4} * \frac{1}{2^{n}-1}$ D. $\frac{7}{8} * \frac{1}{2^{n}-1}$

In a boxing tournament 2n equally skilled players P1,P2,P3...........P$2^{n}$, are participating.In each round players are divided in pairs at random and winner from each...

Samujjal Das

1.1k views

Samujjal Das asked Dec 31, 2016

4 votes

2 answers

812

CMI2016-A-7
Varsha lives alone and dislikes cooking, so she goes out for dinner every evening. She has two favourite restaurants, $\text{Dosa Paradise}$ and $\text{Kababs Unlimited}$, to which she travels by local train. The train to $\text{Dosa Paradise}$ runs every $10$ ... up eating in $\text{Kababs Unlimited}$? $\frac{1}{5}$ $\frac{1}{3}$ $\frac{2}{5}$ $\frac{1}{2}$

Varsha lives alone and dislikes cooking, so she goes out for dinner every evening. She has two favourite restaurants, $\text{Dosa Paradise}$ and $\text{Kababs Unlimited}$...

go_editor

730 views

go_editor asked Dec 30, 2016

0 votes

0 answers

813

http://gateoverflow.in/1177/gate2005-52
How many 2 strings of length n are generated by tossing a coin n times?(Setting value 0 or 1) Is it (2^n+2^n) or (2^n*2^n)?

How many 2 strings of length n are generated by tossing a coin n times?(Setting value 0 or 1)Is it (2^n+2^n) or (2^n*2^n)?

Adiaspirant

195 views

Adiaspirant asked Dec 29, 2016

0 votes

0 answers

814

Is question correct

thor

245 views

thor asked Dec 29, 2016

4 votes

1 answer

815

TIFR CSE 2016 | Part A | Question: 11
In one of the islands that his travels took him to, Gulliver noticed that the probability that a (uniformly) randomly chosen inhabitant has height at least $2$ meters is $0.2$. Also, $0.2$ is the probability that a a (uniformly) randomly ... Which of the above statements is necessarily true? ii only iii only i, ii and iii ii and iii only None of the above

In one of the islands that his travels took him to, Gulliver noticed that the probability that a (uniformly) randomly chosen inhabitant has height at least $2$ meters is ...

go_editor

684 views

go_editor asked Dec 28, 2016

1 votes

1 answer

816

probability
1)For three events A, B and C, we know that A and C are independent B and C are independent A and B are disjoint P(A∪C)=2/3 P(B∪C)=3/4 P(A∪B∪C)=11/12 P(A)=___________ ans 1/3 2)Consider independent trails consisting of rolling a pair of fair dice, over and over. What is the probability that a sum of 5 appears before sum of 7? ans 2/5

1)For three events A, B and C, we know thatA and C are independentB and C are independentA and B are disjointP(A∪C)=2/3 P(B∪C)=3/4 P(A∪B∪C)=11/12P(A)=___________ ...

Neal Caffery

2.9k views

Neal Caffery asked Dec 28, 2016

1 votes

1 answer

817

probability
players P1,P2,P3……… P16 play in a tournament. They are divided into eight pairs at random, from each pair a winner is decided on the basis of a game played between the two players of the pairs. Assuming that all the players are of equal strength, the probability that exactly one of the two players P1 and P2 is among the eight winners is ________.ans 8/15

players P1,P2,P3……… P16 play in a tournament. They are divided into eight pairs at random, from each pair a winner is decided on the basis of a game played between ...

Neal Caffery

524 views

Neal Caffery asked Dec 28, 2016

0 votes

0 answers

818

virtual gate
If we take out two Aces from a standard deck of 52 cards. How many ways are there to select three more cards from the remaining 50, in such a way that the five cards together form a full house (3 of one kind, 2 of another)?

If we take out two Aces from a standard deck of 52 cards. How many ways are there to select three more cards from the remaining 50, in such a way that the five cards toge...

firki lama

322 views

firki lama asked Dec 27, 2016

1 votes

1 answer

819

probability
1) A total of 46% of the voters in a certain city classify themselves as Independents, where as 30% classify themselves as Liberals and 24% say they are Conservatives. In s recent local election, 35% of the Independents, 62% of the Liberals and 58% of ... Given that this child is the eldest child in the family, the conditional probability that the family has 4 children _______.ans 0.18

1) A total of 46% of the voters in a certain city classify themselves as Independents, where as 30% classify themselves as Liberals and 24% say they are Conservatives. In...

Neal Caffery

570 views

Neal Caffery asked Dec 27, 2016

10 votes

3 answers

820

TIFR CSE 2016 | Part A | Question: 4
There are $n$ balls $b_1, \dots ,b_n$ and $n$ boxes. Each ball is placed in box chosen independently and uniformly at random. We say that $(b_i, b_j)$ is a $\textit{colliding pair}$ if $i<j$, and $b_i$ and $b_j$ are placed in the same box. What is the ... $\frac{n-1}{2}$ $0$ $1$ $\frac{n}{4}$ $\begin{pmatrix} n \\ 2 \end{pmatrix}$

There are $n$ balls $b_1, \dots ,b_n$ and $n$ boxes. Each ball is placed in box chosen independently and uniformly at random. We say that $(b_i, b_j)$ is a $\textit{colli...

go_editor

1.9k views

go_editor asked Dec 26, 2016

2 votes

1 answer

821

Maths
There are 2 white and 4 black balls in urn A; in urn B, there are 4 white and 7 black balls. If one ball is randomly replaced from A into B and a ball is drawn from B then find the probability for the ball to be a white one?

There are 2 white and 4 black balls in urn A; in urn B, there are 4 white and 7 black balls. If one ball is randomly replaced from A into B and a ball is drawn from B the...

Anmol Verma

524 views

Anmol Verma asked Dec 25, 2016

1 votes

0 answers

822

Made Easy doubt
A fair coin is tossed until the same result turns up in succession(two head or two tail).Find the probability the number of tosses neede are even.. my approach ..P={P(x=2)+P(x=4)+P(x=6)+...}=0.33 Me answer 2*{P(x=2)+P(x=4)+P(x=6)+...}=0.66 what is the reason of this 2 multiplication?

A fair coin is tossed until the same result turns up in succession(two head or two tail).Find the probability the number of tosses neede are even..my approach ..P={P(x=2)...

Aboveallplayer

495 views

Aboveallplayer asked Dec 23, 2016

15 votes

2 answers

823

TIFR CSE 2017 | Part A | Question: 9
Consider the $majority$ function on three bits, $\textbf{maj}: \{0, 1\}^3 \rightarrow \{0, 1\}$ where $\textbf{maj}(x_1, x_2, x_3)=1$ if and only if $x_1+x_2+x_3 \geq 2$. Let $p(\alpha)$ be the probability that the output is $1$ when each input is set to ... $3 \alpha$ $\alpha^2$ $6\alpha(1-\alpha)$ $3\alpha^2 (1-\alpha)$ $6\alpha(1-\alpha)+\alpha^2$

Consider the $majority$ function on three bits, $\textbf{maj}: \{0, 1\}^3 \rightarrow \{0, 1\}$ where $\textbf{maj}(x_1, x_2, x_3)=1$ if and only if $x_1+x_2+x_3 \geq 2$....

go_editor

1.4k views

go_editor asked Dec 21, 2016

0 votes

2 answers

824

testbook test series
What is the variance of random variable X whose value when two fair dice are rolled is X((i,j)) = i + j , where i and j are the numbers appearing on the first and second die respectively ? a) 35/6 b) 49/4 c) 91/6 d) 35/12

What is the variance of random variable X whose value when two fair dice are rolled is X((i,j)) = i + j , where i and j are the numbers appearing on the first and second ...

Anand Vijayan

880 views

Anand Vijayan asked Dec 19, 2016

4 votes

2 answers

825

Probability ,Settheory.
$1)$ A random selector can only select one of the nine integers $\left \{ 1,2,.....,9 \right \}$ and it makes these selections with equal probability,Assume that $n$ numbers are chosen this way.Find the probability such that the product of $n$ numbers selected is not divisible by $3$. $2)$ Let S = {1, 2, . . . , n} then Find |{(R, T) : R, T ⊆ S, R ∩ T = ∅}| = ?

$1)$ A random selector can only select one of the nine integers $\left \{ 1,2,.....,9 \right \}$ and it makes these selections with equal probability,Assume that $n$ num...

Prabhanjan_1

1.4k views

Prabhanjan_1 asked Dec 19, 2016

1 votes

1 answer

826

Expected value
in C language rand() returns a random integer number. Following is a function definition. int f() { return (rand() & 1) ? 1:0; } Then what will be the expected value of count ? count = 0; for(i=1;i<=n;i++) { if(f() && f()) { count++; } } & is bitwise AND && is logical AND and assume required seed has been initialized.

in C language rand() returns a random integer number. Following is a function definition.int f() { return (rand() & 1) ? 1:0; }Then what will be the expected value of co...

667 views

dd asked Dec 17, 2016

2 votes

1 answer

827

Permutation Combination
If I arrange all 4 digit number format in ascending order then find the rank of the number 3582?

If I arrange all 4 digit number format in ascending order then find the rank of the number 3582?

srestha

797 views

srestha asked Dec 15, 2016

1 votes

2 answers

828

Probablity Problem

KISHALAY DAS

693 views

KISHALAY DAS asked Dec 12, 2016

1 votes

1 answer

829

Poisson Distributions
Customers arrive at a shop according to a Poisson process at rate λ (/min), where they choose to buy either product A (with probability P) or product B (with probability 1 - P), independently. Given that during the first hour 5 customers chose product B, what is the probability ... shop within the first 10 minutes, all bought product A? 60% 70% 30% 40%

Customers arrive at a shop according to a Poisson process at rate λ (/min), where they choose to buy either product A (with probability P) or product B (with probability...

Neal Caffery

789 views

Neal Caffery asked Dec 11, 2016

1 votes

1 answer

830

Probability Density Function

Samujjal Das

536 views

Samujjal Das asked Dec 11, 2016

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