The GATE Grind

GATE 2026 AG – Question 12

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

A box contains one red and two blue balls. After each random draw, the ball is returned. The first two draws were blue. Find the probability the third draw is blue.

  1. 2/3
  2. 1/3
  3. 1/2
  4. 1

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Correct answer: (A) 2/3

Explanation

Replacement restores the same composition before each draw. Therefore the draws are independent, and conditioning on the first two blue outcomes does not change the third-draw chance. There are still two blue balls out of three, so the probability is **2/3, A**.

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