12 grade maths others
The probability that a leap year will have only 52 Sundays is
- A. 4/7
- B. 5/7
- C. 6/7
- D. 1/7
The probability that a leap year will have only 52 Sundays is
- A. 4/7
- B. 5/7
- C. 6/7
- D. 1/7
1 Answer
Askiitians Tutor Team
Approved Tutor Answer9 Months agoThe probability of a leap year having only 52 Sundays can be determined by understanding how many days are in a leap year and how they distribute across the week.
Leap Year Basics
A leap year consists of 366 days, which is 52 weeks and 2 extra days. This means that in a leap year, there are typically 52 Sundays, plus the possibility of 2 additional days that could also be Sundays.
Extra Days Analysis
The two extra days can be any of the following combinations:
- Sunday and Monday
- Monday and Tuesday
- Tuesday and Wednesday
- Wednesday and Thursday
- Thursday and Friday
- Friday and Saturday
- Saturday and Sunday
From these combinations, we can see that only the pairs "Saturday and Sunday" and "Sunday and Monday" include a Sunday. Therefore, there are 2 favorable outcomes where there is an additional Sunday out of a total of 7 possible combinations of extra days.
Calculating the Probability
The probability of having only 52 Sundays is the number of combinations without a Sunday divided by the total combinations:
Probability = (Total combinations - Favorable combinations) / Total combinations
So, the probability is:
Probability = (7 - 2) / 7 = 5/7
Final Answer
The correct answer is B. 5/7.
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