Find the probability of getting 53 Tuesday and 53 Monday in a leap year???

Question

Answer

probability= 2/7

Answer

therefore the answer is 2/7

Answer

but in a leap year there is one more extra day........ therefore there are two extra days that could be any day of the week.Therefore the probability of any day can fit into any of the two days.So probability of getting 53 number of any particular day is 2/7.

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there are a total of 52 complete weeks in a year

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and one day that dies not include in the 52 week.probability of getting a particular day would then be 1/7.

Answer

Introduction:
In a leap year, there are 366 days instead of the usual 365 days. We want to find the probability of getting 53 Tuesdays and 53 Mondays in a leap year. To do this, we need to consider the distribution of weekdays throughout the year and calculate the probability based on those distributions.

Calculating the Probability:

1. Distribution of Weekdays:
In a leap year, the distribution of weekdays is not evenly spread out due to the extra day. We need to determine the number of each weekday that occurs in a leap year.

- There are 52 weeks in a year, so each weekday should occur 52 times. However, since there are 7 weekdays, it is not possible for each weekday to occur exactly 52 times.
- To distribute the remaining day, we can add one extra occurrence of a specific weekday. Let's consider Monday as the extra weekday.

2. Calculating the Probability of 53 Tuesdays:
To calculate the probability of getting 53 Tuesdays, we need to determine the number of ways we can arrange 53 Tuesdays in a leap year.

- Since there are 366 days in a leap year, we need to choose 53 days out of those 366 days to be Tuesdays.
- The number of ways to choose 53 days out of 366 days is given by the binomial coefficient 'C(366, 53)'.
- The total number of possible outcomes is the number of ways to choose any 53 days out of 366.
- Therefore, the probability of getting 53 Tuesdays is: P(53 Tuesdays) = C(366, 53) / C(366, 53) = 1.

3. Calculating the Probability of 53 Mondays:
To calculate the probability of getting 53 Mondays, we need to determine the number of ways we can arrange 53 Mondays in a leap year.

- Since there are 366 days in a leap year, we need to choose 53 days out of those 366 days to be Mondays.
- The number of ways to choose 53 days out of 366 days is given by the binomial coefficient 'C(366, 53)'.
- The total number of possible outcomes is the number of ways to choose any 53 days out of 366.
- Therefore, the probability of getting 53 Mondays is: P(53 Mondays) = C(366, 53) / C(366, 53) = 1.

Conclusion:
In a leap year, the probability of getting 53 Tuesdays and 53 Mondays is 1. This is because the distribution of weekdays in a leap year allows for an extra occurrence of a specific weekday (in this case, Monday). Consequently, the probability of obtaining 53 occurrences of both Tuesday and Monday is certain.

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