What is the probability of getting 53 Mondays in a leap year?
Answers
Answer:
Step-by-step explanation:
total number of days in non-leap year =365
total number of days in leap year =366
total number of Monday occurs in non leap year is 365 / 7 = 52
the remaining days in non leaf year is 2 so its clear
the probability of the 53 Monday in non leaf year is = 2 / 7
Solution:-
We know,
▶1 year has 365 days
▶1 leap year has 366 days(As February has 29 days)
And,
▶Total number of weeks = 52
A week has a Monday for sure.Hence,there will be 52 Mondays.
→ 52 × 7 = 364 days.
Remaining days:-
→ 366 - 364 = 2days
A new year can start with any day out of 7 days.
These two days left can be :-
If the leap year starts with Saturday,then the two days left are:
- Sunday, Monday
If the leap year starts with Sunday,then the two days left are:
- Monday, Tuesday
If the leap year starts with Monday,then the two days left are:
- Tuesday, Wednesday
If the leap year starts with Tuesday,then the two days left are:
- Wednesday, Thursday
If the leap year starts with Wednesday,then the two days left are:
- Thursday, Friday
If the leap year starts with Thursday,then the two days left are:
- Friday, Saturday
If the leap year starts with Friday,then the two days left are:
- Saturday, Sunday
We can observe that ,
▶Total no.of possible cases = 7
▶Favourable outcomes = 2 (As only 2 cases contain monday in the remaining days)
Using the formula,
✦Probability=No.of.favourable outcomes/Total no.of.favourable outcomes
Putting values,
▶Probability = 2/7
Hence, the probability of getting 53 Mondays in a leap year is 2/7.
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