GATE EC || MATHEMATICS || PROBABILITY & STATISTICS || PYQs || 2000-2025

Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability 1/5 of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is ____.

( GATE 2023 || EC || MCQ ||1 MARK)

Suppose  X and  Y are independent and identically distributed random variables that are distributed uniformly in the interval [0, 1] . The probability that X is greater than equal to Y is __

(GATE 2024 || EC || NAT ||1 MARK)

Two fair dice (with faces labeled 1, 2, 3, 4, 5, and 6) are rolled. Let the random variable X  denote the sum of the outcomes obtained. The expectation of  is ___________ (rounded off to two decimal places)

(GATE 2025 || EC || NAT ||1 MARK)

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?

( GATE 2025 || EC || MCQ ||1 MARK)

In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study Commerce. Commerce students are two times more likely to be a boy than are Science students. The amount of information gained in knowing that a randomly selected girl student studies Commerce (rounded off to three decimal places) is _____ bits.

A box contains the following three coins.

I. A fair coin with head on one face and tail on the other face.

II. A coin with heads on both the faces.

III. A coin with tails on both the faces.

A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head the probability of getting a head in the second
toss is

Let X₁, X₂, X₃ and X₄ be independent normal random variables with zero mean and unit variance. The probability that X₄ is the smallest among the four is _

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _____.

Three fair cubical dice are thrown simultaneously. The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place) _____.