CUET UG 2025 — Mathematics Algebra

A leap year has 366 days.

Dividing 366 by 7:

366 ÷ 7 = 52 weeks + 2 extra days

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Since there are 52 complete weeks, there are guaranteed to be 52 Sundays.

Whether there is a 53rd Sunday depends on the 2 extra days.

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The 2 extra consecutive days can be any of these 7 combinations:

1. (Sunday, Monday)
2. (Monday, Tuesday)
3. (Tuesday, Wednesday)
4. (Wednesday, Thursday)
5. (Thursday, Friday)
6. (Friday, Saturday)
7. (Saturday, Sunday)

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Out of 7 possible combinations, Sunday appears in 2 combinations: (Sunday, Monday) and (Saturday, Sunday).

Probability of getting 53 Sundays $= \frac{2}{7}$=72​

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Probability of NOT getting 53 Sundays:

$$= 1 - \frac{2}{7}$$=1−72​

$$= \frac{7-2}{7}$$=77−2​

$$= \frac{5}{7}$$=75​

Therefore, the probability of not getting 53 Sundays in a leap year is $\frac{5}{7}$75​.