GATE AG 2022 • Q12 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Random variables

Question Statement:

The probability of having 53 Sundays in a randomly selected leap year is ______.

Options:

  • (A) 1/7
  • (B) 1/4
  • (C) 2/7
  • (D) 4/7

Official Answer Key:

C

Step-by-Step Solution & Explanation

• A leap year has 366 days = 52 complete weeks + 2 extra days, guaranteeing 52 Sundays already. • The 2 extra days can be one of 7 equally likely consecutive pairs; exactly 2 of these pairs contain a Sunday: (Sun,Mon) and (Sat,Sun). • Probability of 53 Sundays = 2/7.

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