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x/7 is the chance that a leap year, selected at random, will contain 53 Sundays. Find the value of x? (Answer up to the nearest integer)
Correct answer is '2'. Can you explain this answer?
Most Upvoted Answer
x/7 is the chance that a leap year, selected at random, will contain...
Understanding Leap Years
Leap years occur every four years, adding an extra day to the calendar in February. This means that a leap year consists of 366 days instead of the usual 365.
Days in a Leap Year
- A leap year has 52 complete weeks, which account for 364 days.
- The remaining 2 days can fall on any day of the week.
Possibilities for Extra Days
In a leap year, the extra days can be:
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday and Wednesday
4. Wednesday and Thursday
5. Thursday and Friday
6. Friday and Saturday
7. Saturday and Sunday
Counting Sundays
- Out of these combinations, the cases where there are 53 Sundays are:
- (Sunday, Monday)
- (Saturday, Sunday)
Thus, there are 2 favorable outcomes for having 53 Sundays in a leap year.
Total Possible Outcomes
Since there are a total of 7 combinations of the extra days, the probability of having 53 Sundays in a leap year is calculated as follows:
- Probability = Favorable outcomes / Total outcomes = 2 / 7
Finding the Value of x
In the context of the question where the chance of a leap year containing 53 Sundays is expressed as x/7, we can equate:
- x = 2
Therefore, the value of x is 2, which matches the correct answer.
Leap years occur every four years, adding an extra day to the calendar in February. This means that a leap year consists of 366 days instead of the usual 365.
Days in a Leap Year
- A leap year has 52 complete weeks, which account for 364 days.
- The remaining 2 days can fall on any day of the week.
Possibilities for Extra Days
In a leap year, the extra days can be:
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday and Wednesday
4. Wednesday and Thursday
5. Thursday and Friday
6. Friday and Saturday
7. Saturday and Sunday
Counting Sundays
- Out of these combinations, the cases where there are 53 Sundays are:
- (Sunday, Monday)
- (Saturday, Sunday)
Thus, there are 2 favorable outcomes for having 53 Sundays in a leap year.
Total Possible Outcomes
Since there are a total of 7 combinations of the extra days, the probability of having 53 Sundays in a leap year is calculated as follows:
- Probability = Favorable outcomes / Total outcomes = 2 / 7
Finding the Value of x
In the context of the question where the chance of a leap year containing 53 Sundays is expressed as x/7, we can equate:
- x = 2
Therefore, the value of x is 2, which matches the correct answer.
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Community Answer
x/7 is the chance that a leap year, selected at random, will contain...
There are 52 complete weeks in a calendar year i.e. 52 x 7 = 364 days
Number of days in a leap year = 366
∴ Probability of 53 Sundays = 2/7
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x/7 is the chance that a leap year, selected at random, will contain 53 Sundays. Find the value of x? (Answer up to the nearest integer)Correct answer is '2'. Can you explain this answer?
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