Understanding Ordinary Years and Probability

Let's break down the problem of finding the probability of having 53 Tuesdays in an ordinary year. First, we need to know exactly what an ordinary year is and how many days it has. An ordinary year is a year that is not a leap year. It has a fixed number of days, which is important for our probability calculation.

An ordinary year has 365 days.

Probability is a measure of how likely an event is to occur. It is calculated as:

\(\text{Probability} = \frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\)

Calculating Weeks and Remaining Days in an Ordinary Year

Now, let's figure out how many full weeks are in 365 days and if there are any days left over. There are 7 days in a week. We can divide the total number of days by 7.

\(365 \div 7\)

Let's perform the division:

\(365 = 52 \times 7 + 1\)

This tells us that an ordinary year consists of 52 full weeks and 1 extra day.

• Every full week contains exactly one Monday, one Tuesday, one Wednesday, one Thursday, one Friday, one Saturday, and one Sunday.
• So, in 52 full weeks, there are exactly 52 Tuesdays (and 52 of every other day of the week).

Determining the Possibility of 53 Tuesdays

The number of Tuesdays in the year is determined by the 52 Tuesdays in the full weeks plus the day of the week of the single extra day. To have 53 Tuesdays in the ordinary year, the single extra day must be a Tuesday.

The extra day can be any day of the week. The possible outcomes for this extra day are:

• Sunday
• Monday
• Tuesday
• Wednesday
• Thursday
• Friday
• Saturday

There are 7 equally likely possibilities for the single extra day.

Calculating the Probability of 53 Tuesdays

We want the extra day to be a Tuesday. Out of the 7 possible outcomes for the extra day, only one outcome is favourable for having 53 Tuesdays (when the extra day is a Tuesday).

So, the number of favourable outcomes is 1.

The total number of possible outcomes is 7.

Using the probability formula:

\(\text{Probability of 53 Tuesdays} = \frac{\text{Number of favourable outcomes (extra day is Tuesday)}}{\text{Total number of possible outcomes for the extra day}}\)

\(\text{Probability of 53 Tuesdays} = \frac{1}{7}\)

Therefore, the probability of having 53 Tuesdays in an ordinary year is \(\frac{1}{7}\). This straightforward calculation demonstrates how understanding the structure of an ordinary year is key to solving this type of probability problem.