We know that a leap year has 366 days.

So, we have 52 weeks and 2 days. Hence, a leap year has 52 Sundays.

The remaining 2 days can be:

{Sunday,Monday},{Monday,Tuesday},{Tuesday,Wednesday}, Wednesday,Thursday},{Thursday,Friday},{Friday,Saturday},{Saturday,Sunday}

Hence, we have 7 possibilities. From the possibilities, we have two Sundays in it.

Hence, the required probability is 2/7.

Introduction:
A leap year is a year that is evenly divisible by 4, except for years that are divisible by 100. However, years that are divisible by 400 are still considered leap years. In a leap year, there are 366 days instead of the usual 365 days. To find the probability that a leap year, selected at random, will not have 53 Sundays, we need to consider the number of Sundays in a leap year and the total number of possible outcomes.

Number of Sundays in a Leap Year:
Every year has 52 weeks, which means there are 52 Sundays in a non-leap year. In a leap year, there is an extra day, making a total of 366 days. Since 366 is not divisible by 7, there will be 52 complete weeks, and one extra day. This extra day can be any day of the week, including Sunday. Therefore, there can be either 52 or 53 Sundays in a leap year.

Total Number of Possible Outcomes:
To find the total number of possible outcomes, we need to consider the number of days in a leap year. As mentioned earlier, a leap year has 366 days. Each day can be considered as a possible outcome. Therefore, the total number of possible outcomes is 366.

Finding the Probability:
To find the probability that a leap year, selected at random, will not have 53 Sundays, we need to find the number of favorable outcomes and divide it by the total number of possible outcomes.

Favorable Outcomes:
In a leap year, there can be either 52 or 53 Sundays. In this case, we are interested in the number of leap years that have 52 Sundays. Let's assume there are x leap years with 52 Sundays.

Calculating the Probability:
The probability can be calculated using the formula:

Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

In this case, the number of favorable outcomes is x (leap years with 52 Sundays) and the total number of possible outcomes is 366 (days in a leap year). Therefore, the probability can be expressed as:

Probability = x / 366

Conclusion:
To find the probability that a leap year, selected at random, will not have 53 Sundays, we need to calculate the number of leap years with 52 Sundays (favorable outcomes) and divide it by the total number of days in a leap year (possible outcomes). The probability can be expressed as x / 366, where x represents the number of leap years with 52 Sundays.