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Probability — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsProbability1 Mark
MCQ
What is the probability that a non $-$ leap year has $53$ Sundays?
  • A
    $\frac{6}{7}$
  • ✓
    $\frac{1}{7}$
  • C
    $\frac{5}{7}$
  • D
    None of these.
✓

Answer

Correct option: B.
$\frac{1}{7}$
Given : A non leap year
To Find: Probability that a non leap year has $53$ Sundays.
Total number of days in a non leap year is $365$ days
Hence number of weeks in a non leap year is $\frac{365}{7}=52$ weeks and $1$ day
In a non leap year we have $52$ complete weeks and $1$ day which can be any day of the week
i.e. Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday
To make $53$ Sundays the additional day should be Sunday
Hence total number of days which can be any day is $7$
Favorable day i.e. Sunday is $1$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability that a non leap year has $53$ Sundays is
Hence the correct option is $b.$

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