Question

The probability that a leap year will have only 52 Sunday is:
A. $\dfrac{4}{7}$
B. $\dfrac{5}{7}$
C. $\dfrac{6}{7}$
D. $\dfrac{1}{7}$

Answer 1

Hint: In order to this question, to find the probability that a leap year will have only 52 Sunday, we will first find the number of weeks a leap year contains, and then we will write the possible pairs of days of the remaining 2 days except 52 weeks of a leap year. And then we will find the probability of not getting the Sunday in the last two days.

Complete step by step answer:
As we know, the number of days in a leap year is 366.
And, the number of weeks $ = \dfrac{{366}}{7} = 52.28 \approx 52weeks$
So, 52weeks and 2days are there in a leap year. And, also 52 Sundays, a leap year.
Now, the probability will also depend on the remaining 2 days.

Now, we will write the possible pair of days that remaining days are:-
(Sunday,Monday), (Monday,Tuesday), (Tuesday,Wednesday), (Wednesday,Thursday), (Thursday,Friday), (Friday,Saturday), (Saturday,Sunday).
So, there are a total 7 days that the remaining 2 days will be, and only 2 pairs of SUNDAY. The remaining 5 pairs don't contain Sunday. Thus, the probability of not getting Sunday in the last two days is $\dfrac{5}{7}$ .

Therefore, the probability of only 52 Sundays in a Leap Year is $\dfrac{5}{7}$.

Hence, the correct option is B.

Note: When an event is certain to occur, the probability of that event occurring is 1, and when the event is definite not to occur, the probability of that event occurring is 0. As a result, the probability value ranges from 0 to 1.