Understanding the Probability of 53 Sundays in 2020

To determine the probability of having 53 Sundays in the year 2020, we first need to understand the nature of the year 2020 and how many days it contains. This is crucial for calculating the probability accurately.

Year 2020: A Leap Year Analysis

The year 2020 is a leap year. A leap year occurs every four years and has 366 days, unlike a common year which has 365 days. We can confirm this because 2020 is perfectly divisible by 4.

• Number of days in a common year = 365 days
• Number of days in a leap year (like 2020) = 366 days

Calculating Weeks and Remaining Days

Next, we determine how many full weeks are present in 366 days and how many days are left over. Since there are 7 days in a week, we perform a division:

\(\frac{366 \text{ days}}{7 \text{ days/week}} = 52 \text{ weeks and } 2 \text{ days remaining}\)

This means that every year, regardless of whether it's a common or a leap year, will have at least 52 Sundays. The question of having 53 Sundays depends entirely on the two remaining days in a leap year.

Identifying Possible Outcomes for Remaining Days

The 52 full weeks account for 52 Sundays. For there to be a 53rd Sunday, one of the two remaining days must be a Sunday. Let's list all the possible combinations for these two consecutive remaining days:

There are 7 distinct possible outcomes for the two remaining days.

Determining Favorable Outcomes for 53 Sundays

For the year 2020 to have 53 Sundays, one of the two extra days must be a Sunday. Looking at our list of possible pairs, the favorable outcomes are:

• (Saturday, Sunday)
• (Sunday, Monday)

There are 2 favorable outcomes where a Sunday is included in the remaining two days.

Calculating the Probability

The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

Probability (\(P\)) = \(\frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}\)

In this case:

• Number of Favorable Outcomes (pairs containing a Sunday) = 2
• Total Number of Possible Outcomes (all pairs of consecutive days) = 7

Therefore, the probability of being 53 Sundays in the year 2020 is:

\(P(\text{53 Sundays in 2020}) = \frac{2}{7}\)

This means there is a 2 out of 7 chance that the year 2020 had 53 Sundays.