53 Mondays in a leap year — Probability Aptitude Question
53 Mondays in a leap year: What is the probability that a leap year chosen at random has 53 Mondays? Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the probability that a leap year chosen at random has 53 Mondays?
Options
- 1/7
- 2/7
- 3/7
- 1/2
Show the answer and the worked solution
Correct answer: B. 2/7
Worked solution
- 366 = 52 × 7 + 2, so every weekday occurs 52 times plus two consecutive extra days.
- The extra pair is one of 7 equally likely consecutive pairs, and 2 of them contain a Monday.
- Probability = 2/7.
Answer: 2/7.
The idea
A leap year has 2 spare days and an ordinary year 1, so the probability of 53 of a given weekday is 2/7 and 1/7 respectively.
Shortcut. The two spare days are different weekdays, each a Monday with chance 1/7, and they cannot both be Monday, so the chances simply add: 1/7 + 1/7 = 2/7.
Common trap. "1/7" — using the ordinary-year answer with one spare day; 366 = 52 weeks + 2 days, so a leap year has two spare days.