MCQ
What is the probability that a leap year has $52$ Mondays ?
- A$\frac{2}{7}$
- B$\frac{4}{7}$
- ✓$\frac{5}{7}$
- D$\frac{6}{7}$
✓
Answer
Correct option: C.
$\frac{5}{7}$
Given : A leap year
To Find : Probability that a leap year has $52$ Mondays.
Total number of days in leap year is $366$ days
Hence number of weeks in a leap year is $\frac{366}{7}=52$ weeks and $2$ day
In a leap year we have $52$ complete weeks and $2$ day which can be any pair of the day of the week i.e.
$($Sunday, Monday$)$
$($Monday, Tuesday$)$
$($Tuesday, Wednesday$)$
$($Wednesday, Thursday$)$
$($Thursday, Friday$)$
$($Friday, Saturday$)$
$($Saturday, Sunday$)$
To make $52$ Mondays the additional days should not include Monday
Hence total number of pairs of days is $7$
Favorable day i.e. in which Mondays is not there is $5$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability that a leap year has $52$ Mondays is equal to $\frac{5}{7}$
Hence the correct option is $c$.
To Find : Probability that a leap year has $52$ Mondays.
Total number of days in leap year is $366$ days
Hence number of weeks in a leap year is $\frac{366}{7}=52$ weeks and $2$ day
In a leap year we have $52$ complete weeks and $2$ day which can be any pair of the day of the week i.e.
$($Sunday, Monday$)$
$($Monday, Tuesday$)$
$($Tuesday, Wednesday$)$
$($Wednesday, Thursday$)$
$($Thursday, Friday$)$
$($Friday, Saturday$)$
$($Saturday, Sunday$)$
To make $52$ Mondays the additional days should not include Monday
Hence total number of pairs of days is $7$
Favorable day i.e. in which Mondays is not there is $5$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability that a leap year has $52$ Mondays is equal to $\frac{5}{7}$
Hence the correct option is $c$.
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