What is the probability that on ordinary year has 53 Tuesdays ?

Explanation

To determine the probability that an ordinary year has 53 Tuesdays, we first need to understand how many days are in an ordinary year and how the days of the week are distributed.

### Step 1: Understand the number of days in an ordinary year
An ordinary year has 365 days.

**Hint:** Remember that a week has 7 days.

### Step 2: Calculate the number of weeks in an ordinary year
To find out how many complete weeks are in 365 days, we divide 365 by 7.

\[ \text{Number of weeks} = \frac{365}{7} = 52 \text{ weeks} \text{ and } 1 \text{ day} \]

**Hint:** When you divide, note the quotient and the remainder.

### Step 3: Determine the distribution of days
Since there are 52 complete weeks, each day of the week (Monday, Tuesday, ..., Sunday) will occur 52 times. The extra day (the remainder from the division) will determine if there is an additional occurrence of a specific day.

**Hint:** Think about how the extra day affects the count of each day of the week.

### Step 4: Identify the extra day
The extra day can be any one of the 7 days of the week. Therefore, the extra day could be:
- Sunday
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday

**Hint:** List out the days of the week to visualize this.

### Step 5: Count the occurrences of Tuesdays
If the extra day is a Tuesday, then there will be 53 Tuesdays in that year. If the extra day is any other day, there will only be 52 Tuesdays.

**Hint:** Consider how many scenarios lead to having 53 Tuesdays.

### Step 6: Calculate the probability
Since there are 7 possible days for the extra day, and only 1 of those days (Tuesday) results in having 53 Tuesdays, the probability can be calculated as follows:

\[ \text{Probability of 53 Tuesdays} = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{1}{7} \]

**Hint:** Remember the formula for probability: P(Event) = (Number of favorable outcomes) / (Total possible outcomes).

### Final Answer
The probability that an ordinary year has 53 Tuesdays is \(\frac{1}{7}\).

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