Q. 25

# Mark the correct alternative in each of the following:The probability that in a year of 22nd century chosen at random, there will be 53 Sundays, isA. 3/28B. 2/28C. 7/28D. 5/28

P(53 Sundays) = P(Leap Years)P(53 Sundays in a Leap Year) + P(Non-Leap Years)P(53 Sundays in a Non-Leap Year) (1)

Now,

P(53 Sundays in a Leap Year) (52 Weeks + 2 days Saturday + Sunday or Sunday + Monday)

P(53 Sundays in a non-Leap Year) (52 Weeks + 1 day)

Next step in solving this problem requires the total number of leap years in 22nd Century.

Leap Years = 24

Non Leap Years = 76

P(Leap Year)

P(Non-Leap Year)

We now have all the required information, using equation (1) we get

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