The probability that a leap year will have 53 Fridays or 53 Satur… - Vidyadip

MCQ

The probability that a leap year will have 53 Fridays or 53 Saturdays is:

A
$\frac{2}{7}$
✓
$\frac{3}{7}$
C
$\frac{4}{7}$
D
$\frac{1}{7}$

✓

Answer

Correct option: B.

$\frac{3}{7}$

We know that a leap year has 366 days (i.e. 7 × 52 + 2) = 52 weeks and 2 extra days .
The sample space for these 2 extra days is given below:
S = {(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday), (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)} There are 7 cases.
$\therefore\text{n(S)}=7$
Let E be the event that the leap year has 53 Fridays or 53 Saturdays.
E = { (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}
i.e. n(E) = 3
$\therefore\text{P(E)}=\frac{\text{n(E)}}{\text{n(S)}}=\frac{3}{7}$
Hence, the probability that a leap year has 53 Fridays or 53 Saturdays is $\frac{3}{7}$.

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