Question

What is the probability that a leap year has 53 Sundays?
A. $${\displaystyle \frac{1}{7}}$$
B. $${\displaystyle \frac{12}{52}}$$
C. $${\displaystyle \frac{2}{7}}$$
D. $${\displaystyle \frac{1}{52}}$$

Answer 1

Hint:-Probability is the number of ways of achieving success upon the total number of possible outcomes.In a leap year we have 366 days, therefore it will have 52 weeks and 2 days. The sample space of having Sunday or chances of having Sunday on those two days are written which gives a favourable number of outcomes and total number of sample space of two days gives total number of outcomes. Then the ratio of favourable outcomes and total number of outcomes gives probability.

Complete step-by-step answer:
A leap year has 366 days.
Therefore, it will have 52 weeks and 2 days.
These 2 days may be:-
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday and Wednesday
4. Wednesday and Thursday
5. Thursday and Friday
6. Friday and Saturday
7. Saturday and Sunday

So, there are seven possibilities.
Out of these seven possibilities, two of them favor the event that one of the two days is a Sunday.
We know that the formula to find probability is NUMBER OF FAVORABLE OUTCOMES UPON TOTAL NUMBER OF POSSIBLE OUTCOMES
Therefore, as the number of total possible outcomes is seven and the number of favorable outcomes is two, thus, the probability that a leap year has 53 Sundays is $${\displaystyle \frac{2}{7}}$$.
Hence, the answer of this question is C
 $${\displaystyle \frac{2}{7}}$$ .

NOTE:-
One must always remember that the formula to calculate the probability is:-
$$={\displaystyle \frac{favorableoutcomes}{totaloutcomes}}$$
The student should know the formulas and definitions of probability and also knowledge of finding the sample space for a given question.