Leap year or not

Probability Level 2

What is the probability that any given year is a leap year?

Note : The criteria for an year to be leap year is :

(i) - The year should be divisible by 4.

(ii) - If the year is divisible by 100, it's not a leap year (eg. 1900).

(ii) - If the year is divisible by 400, it's a leap year (eg. 2000).

99/400 1/4 103/400 97/400

Aviral Pandey by Aviral Pandey , 27, India

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1 solution

Jerry McKenzie
Jan 25, 2018

Note condition (iii) shows the cycle repeats every 400 years. Thus in 400 years we can find that there are 400/4=100 usual leap years (of set A) minus 400/100=4 skipped leap years (of set B) plus 400/400=1 of the third condition (of set C)

Note for any two sets if B ⊆ A B \subseteq A then B ⋂ A = B B \bigcap A = B and B ⋃ A = A B \bigcup A = A

We add and subract because we counted the centuries (100) already when we checked divisibility by 4, and we had to re-include the one divisible by 400.

This leads to (100-4+1)/400 = 97/400

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1 Helpful 0 Interesting 0 Brilliant 0 Confused

Sir, the second note should be,

(ii) - If the year is divisible by 100, it's not necessarily a leap year (eg. 1900).

Aryan Sanghi - 3 years, 4 months ago

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