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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

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

Recent questions in Probability

0 votes
1 answer
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1 vote
1 answer
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If a random coin is tossed $11$ times, then what is the probability that for $7$th toss head appears exactly $4$ times? $5/32$ $15/128$ $35/128$ None of the options
asked Mar 31 in Probability Lakshman Patel RJIT 73 views
1 vote
1 answer
3
If $X, Y$ and $Z$ are three exhaustive and mutually exclusive events related with any experiment and the $P\left(X \right)=0.5P\left(Y \right)$ and $P\left(Z \right)$ = $0.3P\left(Y \right)$. Then $P\left(Y \right)$ = ___________ . $0.54$ $0.66$ $0.33$ $0.44$
asked Mar 31 in Probability Lakshman Patel RJIT 64 views
0 votes
2 answers
4
A box contains $10$ screws, $3$ of which are defective. Two screws are drawn at random with replacement. The probability that none of two screws is defective will be $100\%$ $50\%$ $49\%$ None of these.
asked Mar 31 in Probability Lakshman Patel RJIT 162 views
1 vote
1 answer
5
The probability that top and bottom cards of a randomly shuffled deck are both aces is: $4/52\times 4/52$ $4/52\times 3/52$ $4/52\times 3/51$ $4/52\times 4/51$
asked Mar 30 in Probability Lakshman Patel RJIT 108 views
1 vote
1 answer
6
A box contains six red balls and four green balls. Four balls are selected at random from the box. What is the probability that two of the selected balls are red and two are green ? $\large\frac{3}{7}$ $\large\frac{4}{7}$ $\large\frac{5}{7}$ $\large\frac{6}{7}$
asked Mar 28 in Probability jothee 127 views
5 votes
4 answers
7
Let $\mathcal{R}$ be the set of all binary relations on the set $\{1,2,3\}$. Suppose a relation is chosen from $\mathcal{R}$ at random. The probability that the chosen relation is reflexive (round off to $3$ decimal places) is ______.
asked Feb 12 in Probability Arjun 1.9k views
2 votes
1 answer
8
Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above
asked Feb 11 in Probability Lakshman Patel RJIT 114 views
0 votes
2 answers
9
In a certain year, there were exactly four Fridays and exactly four Mondays in January. On what day of the week did the $20^{th}$ of the January fall that year (recall that January has $31$ days)? Sunday Monday Wednesday Friday None of the others
asked Feb 10 in Probability Lakshman Patel RJIT 222 views
1 vote
2 answers
10
A lottery chooses four random winners. What is the probability that at least three of them are born on the same day of the week? Assume that the pool of candidates is so large that each winner is equally likely to be born on any of the seven days of the week independent of the other winners. ... $\dfrac{48}{2401} \\$ $\dfrac{105}{2401} \\$ $\dfrac{175}{2401} \\$ $\dfrac{294}{2401}$
asked Feb 10 in Probability Lakshman Patel RJIT 188 views
0 votes
0 answers
11
Fix $n\geq 4.$ Suppose there is a particle that moves randomly on the number line, but never leaves the set $\{1,2,\dots,n\}.$ Let the initial probability distribution of the particle be denoted by $\overrightarrow{\pi}.$ In the first step, if the particle is at position $i,$ it moves to one ... $i\neq 1$ $\overrightarrow{\pi}(n) = 1$ and $\overrightarrow{\pi}(i) = 0$ for $i\neq n$
asked Feb 10 in Probability Lakshman Patel RJIT 84 views
1 vote
2 answers
12
Two balls are drawn uniformly at random without replacement from a set of five balls numbered $1,2,3,4,5.$ What is the expected value of the larger number on the balls drawn? $2.5$ $3$ $3.5$ $4$ None of the above
asked Feb 10 in Probability Lakshman Patel RJIT 172 views
0 votes
1 answer
13
For the distributions given below : Which of the following is correct for the above distributions? Standard deviation of $A$ is significantly lower than standard deviation of $B$ Standard deviation of $A$ is slightly lower than standard deviation of $B$ Standard deviation of $A$ is same as standard deviation of $B$ Standard deviation of $A$ is significantly higher than standard deviation of $B$
asked Jan 13 in Probability Satbir 439 views
1 vote
0 answers
14
So, I have read the birthday paradox problem, and now I came across below question: Assuming the following: there are no leap years, all years have $n = 365$ days and that people's birthdays are uniformly distributed across the $n$ days of the year. (i) How many people must be there in a ... $n=23$, this works out to be 0.53 and Yes it seems to me I am done. Please correct me If I am wrong.
asked Nov 12, 2019 in Probability Ayush Upadhyaya 235 views
1 vote
0 answers
15
Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the first 20 days? (b) What is the probability of getting 10 Heads before 5 Tails?
asked Oct 23, 2019 in Probability ajaysoni1924 191 views
0 votes
1 answer
16
A permutation of $1,2, \dots, n$ is chosen at random. Then the probability that the numbers $1$ and $2$ appear as neighbour equals $\frac{1}{n}$ $\frac{2}{n}$ $\frac{1}{n-1}$ $\frac{1}{n-2}$
asked Sep 23, 2019 in Probability Arjun 269 views
1 vote
1 answer
17
Two coins are tossed independently where $P$(head occurs when coin $i$ is tossed) $=p_i, \: i=1,2$. Given that at least one head has occurred, the probability that coins produced different outcomes is $\frac{2p_1p_2}{p_1+p_2-2p_1p_2}$ $\frac{p_1+p_2-2p_1p_2}{p_1+p_2-p_1p_2}$ $\frac{2}{3}$ none of the above
asked Sep 23, 2019 in Probability Arjun 203 views
2 votes
1 answer
18
The number of cars $(X)$ arriving at a service station per day follows a Poisson distribution with mean $4$. The service station can provide service to a maximum of $4$ cars per day. Then the expected number of cars that do not get service per day equals $4$ $0$ $\Sigma_{i=0}^{\infty} i P(X=i+4)$ $\Sigma_{i=4}^{\infty} i P(X=i-4)$
asked Sep 23, 2019 in Probability Arjun 250 views
1 vote
1 answer
19
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
asked Sep 18, 2019 in Probability gatecse 100 views
1 vote
2 answers
20
A basket contains some white and blue marbles. Two marbles are drawn randomly from the basket without replacement. The probability of selecting first a white and then a blue marble is $0.2$. The probability of selecting a white marble in the first draw is $0.5$. What is the probability of ... a blue marble in the second draw, given that the first marble drawn was white? $0.1$ $0.4$ $0.5$ $0.2$
asked Sep 18, 2019 in Probability gatecse 146 views
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