Question

What is the probability that a leap year has 53 Sundays?
A. $\dfrac{1}{7}$
B. $\dfrac{2}{7}$
C. $\dfrac{1}{{52}}$
D. $\dfrac{1}{{365}}$

Answer 1

Hint: There are $366$ days in leap year means $52$ weeks and $2$ extra days. Make the possibilities for two extra days and evaluate the probability.
Probability of any event A is defined as the ratio of the favourable outcomes to the total outcomes. The formula for the probability of A will be:
\[P(A) = \dfrac{{Favourable\,Outcomes}}{{Total\,Outcomes}}\]

Complete step-by-step answer:
We have given a leap year.
We have to evaluate the probability that a leap year has $53$ Sundays.
The difference between the leap and normal year is that the number of days in normal year is $365$ and the number of days in leap year is $366$
Therefore, in the leap year there are $52$ weeks and $2$ extra days. It means $52$ Sundays are included.
We have to make the conditions for $2$ extra days and our favourable outcomes will consist of $1$ Sunday so that total Sundays will be $53$.
The possibilities for two extra days will be:
{Monday, Tuesday}, {Tuesday, Wednesday}, {Wednesday, Thursday}, {Thursday, Friday}, {Friday, Saturday}, {Saturday, Sunday} and {Sunday, Monday}
In two of the cases {Saturday, Sunday} and {Sunday, Monday}, Sunday is present, therefore favourable outcomes will be $2$ and total possibilities are $7$, therefore, total outcomes will be $7$.
We know that probability of any event A is defined as the ratio of the favourable outcomes to the total outcomes. The formula for the probability of A will be:
\[P(A) = \dfrac{{Favourable\,Outcomes}}{{Total\,Outcomes}}\]
Therefore, the probability of $53$ Sundays in a leap year is $\dfrac{2}{7}$.

So, the correct answer is “Option B”.

Note: In these types of questions the total outcomes will not be equal to the total number of days because in $365$ days, the number of Sundays are fixed. Therefore, the total outcomes will come from $2$ extra days.