GATE|| Engineering Mathematics || Probability & Statistics || Pyqs (2010 to 2025 )

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Question 1

In an examination, a student can choose the order in which two questions (Ques A and Ques B) must be attempted.

      - If the first question is answered wrong, the student gets zero marks. 

      - If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question. 

      - If both the questions are answered correctly, the student gets the sum of the marks of the two questions. 

The following table shows the probability of correctly answering a question and the marks of the question respectively.

Screenshot-2025-08-21-183040

Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?

 [ MCQ || GATE 2021 Set-2 || 2 Marks]

  • First QuesB and then QuesA. Expected marks 14.

  • First QuesB and then QuesA. Expected marks 22.

  • First QuesA and then QuesB. Expected marks 16.

  • First QuesA and then QuesB. Expected marks 14.

Question 2

Consider the following experiment.

 Step1. Flip a fair coin twice.      
Step2. If the outcomes are (TAILS, HEADS) then output Y and stop.      
Step3. If the outcomes are either (HEADS, HEADS) or (HEADS, TAILS), then output N and stop.      
Step4. If the outcomes are (TAILS, TAILS), then go to Step 1.

The probability that the output of the experiment is Y is (up to two decimal places) ________.

[ NAT || GATE 2016 Set-1 || 2 Marks]


  • 0.33

Question 3

P and Q are considering to apply for job. The probability that p applies for job is 1/4. The probability that P applies for job given that Q applies for the job 1/2 and The probability that Q applies for job given that P applies for the job 1/3.The probability that P does not apply for job given that Q does not apply for the job

[ MCQ || GATE 2017 Set-2 || 2 Marks]

  • 4/5

  • 5/6

  • 7/8

  • 11/12

Question 4

Screenshot-2025-10-29-160734


[ MCQ || GATE 2017 Set-2 || 2 Marks]

  • Nβ (1 – β)

  • Nβ

  • N (1 – β)

  • Not expressible in terms of N and β alone

Question 5

If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X + 2)2] equals _______. [ NAT || GATE 2017 Set-2 || 2 Marks]

  • 54

Question 6

Let X be a Gaussian random variable with mean 0and variance σ2. Let Y = max(X, 0) where max(a,b) is the maximum of a and b. The median of Y is __________.

[ NAT || GATE 2017 Set-1 || 1 Marks]


  • 0

Question 7

Two people, P and Q, decide to independently roll two identical dice, each with 6 faces, numbered 1 to 6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by P and Q. Assume that all 6 numbers on each dice are equi-probable and that all trials are independent. The probability (rounded to 3 decimal places) that one of them wins on the third trial is __________.

[ NAT || GATE 2018 || 1 Marks]

  • 0.023

Question 8

Consider the two statements.

S1 : There exist random variables X and Y such that

      (E[(X – E(X)) (Y – E(Y))])2> Var[X] Var[Y]

S2 : For all random variables X and Y,

      Cov[X,Y] = E[|X – E[X]||Y – E[Y]|]

Which one of the following choices is correct? [ MCQ || GATE 2021 Set-1 || 2 Marks]

  • Both S1 and S2 are true

  • S1 is true, but S2 is false.

  • Both S1 and S2 are false.

  • S1 is false, but S2 is true

Question 9

A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour.

Note that the number of balls in the bag will increase by one after each trial.

A sequence of four such trials is conducted.

Which one of the following choices gives the probability of drawing a red ball in the fourth trial?

[ MCQ || GATE 2021 Set-2 || 2 Marks]

  • r/(r + b)

  • r/(r + b + 3)

  • (r + 3)/(r + b + 3)

  • .

    Screenshot-2025-08-21-182746


Question 10

A probability density function on the interval [a,1] is given by 1/x2 and outside this interval the value of the function is zero. The value of a is _________.

[ NAT || GATE 2016 Set-1 || 1 Marks]

  • 0.5

There are 35 questions to complete.

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