Probability that a leap year selected at random contains either 53 Tuesdays or Wednesdays is (a)

step 1 So in the given question we are told to find the probability that a leap year, a leap year selec

Probability that a leap year selected at random contains...

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Key Concepts

Leap Year

A leap year is a year that has an extra day added to keep the calendar year synchronized with the astronomical year. This results in a total of 366 days, which is 52 full weeks plus 2 additional days.

Extra Days in a Leap Year

In a leap year, with its 52 complete weeks, each day of the week naturally occurs 52 times. The 2 extra days are consecutive and depend on the day the year starts. This means that two specific weekdays will occur 53 times, while the remaining five will occur only 52 times.

Uniform Distribution of Starting Days

The starting day of a leap year is equally likely to be any of the seven days of the week. This uniform probability allows us to analyze the problem by considering all 7 possible outcomes for the first day of the year.

Counting Favorable Outcomes

The problem involves counting the cases in which the pair of extra days includes either Tuesday or Wednesday. By considering each possible starting day and checking if Tuesday or Wednesday is included among the extra days, one can determine the number of favorable outcomes. The probability is then calculated by dividing the number of favorable starting days by the total number of days in a week.

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