GATE Probability: Events and Conditional Probability – Previous Year Questions

7 GATE previous year questions on Events and Conditional Probability (Probability, Statistics) with answers and explanations, from every paper.

1. GATE 2021 ST Q24 (1 mark, Numerical answer) – Events A,B satisfy P(B)=3/4 and P(A∪Bᶜ)=1/2. If A and B are independent,find P(A),to two decimals.
2. GATE 2021 ST Q25 (1 mark, Numerical answer) – A fair die is rolled twice independently,giving X,Y. Find E[X+Y (X−Y)²=1].
3. GATE 2021 ST Q43 (2 marks, Multiple choice) – On sample space ℕ,let P(n)=a n. Which statement is NOT true?
4. GATE 2023 ST Q31 (1 mark, Numerical answer) – Two of five bulbs are defective. Bulbs are chosen uniformly without replacement and tested one at a time. Let X be the minimum number of tests needed…
5. GATE 2023 ST Q60 (2 marks, Numerical answer) – On Ω=1,2,3,4,let 𝒢=∅,Ω,1,4,2,3,1,4,1,2,3,2,3,4. Suppose P(1)=1/4 and X(1)=1,X(2)=X(3)=2,X(4)=3. If P(X≤2)=3/4,find P(1,4) to two decimals.
6. GATE 2024 ST Q18 (1 mark, Multiple choice) – Independent fair red and blue dice are thrown once. A:red die is 5 or 6; B:sum is 7; C:sum is 8. Which holds?
7. GATE 2026 ST Q40 (2 marks, Multiple choice) – On Ω let the σ-algebra be Ω,∅,A,Aᶜ, with P(A)=P(Aᶜ)=1/2 and both sets nonempty. Let X=1 A,Y=1 (Aᶜ). Which holds?