Question

The probability that a leap year will have only $52$ Sundays is

• A. $\frac{4}{7}$
• B. $\frac{5}{7}$
• C. $\frac{6}{7}$
• D. $\frac{1}{7}$

Answer 1

Answer: (B)

$\frac{5}{7}$

No. of days in a leap $=366$

$(\frac{366}{7}=52.28)$
So, there will be $52$ weeks and $2$ days

So, every leap year has $52$ Sundays

Now, the probability depends on remaining $2$ days

The possible pairing of days are

Sunday-Monday

Monday-Tuesday

Tuesday-Wednesday

Wednesday-Thursday

Thursday-Friday

Friday-Saturday

Saturday-Sunday

There are total $7$ pairs and out of $7$ pairs, only $2$ pairs have Sunday. The remaining $5$ pairs does not include Sunday
Thus, the probability of not getting Sunday in the last $2$ days is $\frac{5}{7}$

Therefore, the probability of only $52$ Sundays in a Leap year is $\frac{5}{7}$.