The probability that a normal (ordinary) year selected at random will have 53 Saturdays as well as 53 Sundays is?
Understand the Problem
The question is asking for the probability that a randomly selected normal (ordinary) year will have 53 Saturdays and 53 Sundays. This requires understanding the distribution of days in a year.
Answer
The probability is $0$.
Answer for screen readers
The probability that a normal (ordinary) year selected at random will have 53 Saturdays as well as 53 Sundays is $0$.
Steps to Solve
- Understanding the Basics of a Normal Year
A normal year has 365 days, which can be divided into 52 weeks plus 1 extra day. This means there are 52 complete weeks (which include 52 Saturdays and 52 Sundays) plus one additional day.
- Identifying the Extra Day
The extra day can be any of the seven days of the week:
- Sunday
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
This means the possible scenarios for having 53 Saturdays and 53 Sundays are:
- If the extra day is Saturday, there will be 53 Saturdays and 52 Sundays.
- If the extra day is Sunday, there will be 52 Saturdays and 53 Sundays.
- If the extra day is any other day (Monday to Friday), there will still be 52 Saturdays and 52 Sundays.
- Calculating Probability
In total, there are 7 possible outcomes for the extra day. Out of these, there are:
- 1 outcome for 53 Saturdays (extra day is Saturday)
- 1 outcome for 53 Sundays (extra day is Sunday)
Thus, there are no outcomes where a year has both 53 Saturdays and 53 Sundays.
The probability can be calculated as follows:
$$ P(53 \text{ Saturdays and } 53 \text{ Sundays}) = \frac{0}{7} = 0 $$
The probability that a normal (ordinary) year selected at random will have 53 Saturdays as well as 53 Sundays is $0$.
More Information
In normal years, it is impossible for there to be 53 Saturdays and 53 Sundays simultaneously because a normal year has only one extra day compared to complete weeks. Thus, one will always be limited to 52 occurrences of one day of the week.
Tips
- Misunderstanding the Total Days: Some might think there can be multiple extra days in a normal year, but it’s fixed to one extra day.
- Confusion Over Counting Outcomes: It's important to correctly label possible outcomes. The extra day must be recognized correctly in calculations.
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