Question

probability of a month of January having 5 sunday​

Answer 1

           

Answer: 3/7

     

                     

Step-by-step explanation:

         

We know that January has 31 days.

It contains 4 weeks and 3 odd days.

[Odd days are remaining days after weeks.]

As it contains 4 weeks and 3 odd days, any three consecutive days will occur 5 times.

If any doubt, see January 2019 in calendar. It contains 5 Tuesdays, 5 Wednesdays and 5 Thursdays. But other days are of 4 times.

Okay. Following are the 7 total possibilities of 5 days in January:

1. 5 Sundays, Mondays and Tuesdays.
2. 5 Mondays, Tuesdays and Wednesdays.
3. 5 Tuesdays, Wednesdays and Thursdays.
4. 5 Wednesdays, Thursdays and Fridays.
5. 5 Thursdays, Fridays and Saturdays.
6. 5 Fridays, Saturdays and Sundays.
7. 5 Saturdays, Sundays and Mondays.

Among these 7 total possibilities, 5 Sundays are appearing in 3 outcomes.

1. 5 Sundays, Mondays and Tuesdays.
2. 5 Fridays, Saturdays and Sundays.
3. 5 Saturdays, Sundays and Mondays.

So the probability is 3/7.

Plz ask me if you have any doubts.

Thank you. :-))