Question

Assertion (A): The probability that a leap year has 53 Sundays is `2/7`.

Reason (R): The probability that a non-leap year has 53 Sundays is `5/7`.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Assertion (A) is true but Reason (R) is false.

Explanation:

Total number of days in a leap year = 366

Total number of days in a week = 7

∴ Number of Sundays in a year = `366/7`

= 52 Sundays + 2 days

Total number of possible outcomes with 2 days = 7

{(Sunday, Monday), (Monday, Tuesday), (Tuesday, Wednesday), (Wednesday, Thursday) (Thursday, Friday), (Friday, Saturday), (Saturday, Sunday)}

∴ Required probability

= `"No. of favourable outcomes"/"Total number of outcomes"`

= `2/7`

∴ Assertion is true.

Also, Total number of days in a non-leap year = 365

Total number of days in a week = 7

∴ Number of Sundays in a non-leap year = `365/7`

= 52 Sundays + 1 days

1 day can be Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

Hence, the probability of getting 53 Sundays = `1/7`