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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.
Solution
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`
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