Question

Find the probability of having 5 Sundays in the month of February in leap years 2004.
A) $\dfrac{2}{7}$
B) 0
C) $\dfrac{1}{7}$
D) 1

Answer 1

Here we will first write the definition of the leap year. Then we will find the number of weeks in the month of February. Then we will see the number of the possibility of the day 29 of February. Then we will find the probability of the last day being Sunday which will be the required probability.

Complete Step by step Solution:
It is given that the year 2004 is a leap year.
Leap year is a year in which the number of days in the month of February is 29.
We will find the number of weeks in the month of February. We know that there are seven days in a week i.e. 1week $=$ 7days. Therefore, we get
Number of weeks in February is 4 weeks as 4 week $= 4 \times 7 = 28$ days.
And we can see that there is one day left as $29 - 28 = 1$ day.
So this day can be any day i.e. Monday or Tuesday or Wednesday or Thursday or Friday or Saturday or Sunday i.e. either from the 7.
So to get the 5 Sundays in the month of February which means this last day must be Sunday.
Therefore, the probability of the last day being Sunday is $\dfrac{1}{7}$.
Hence the probability of having 5 Sundays in the month of February in leap years 2004 is $\dfrac{1}{7}$.

So, option C is the correct option.

Note:
Here we have to keep in mind that the probability of occurrence is always less than or equal to one. If the probability of the event is one then that event is known as the true event. We should also note that the sum of the probability of occurrence of an event and sum of the probability of not occurrence of an event are always equal to one. We used the same concept to find our required probability. We use the probability concept in our day to day life also like in weather forecasting, clearing an exam, winning a card game etc.