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Question

A probability that in a year of the 22nd century chosen at random, there will be 53 Sundays is


A

328

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B

228

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C

728

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D

528

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Solution

The correct option is D

528


Explanation for the correct option:

Step 1: Find the probability of a leap year:

Estimate the probability that the selected year is a leap year in the century.

As in every four years, there is a leap year.

So in 100 years, there will be 25 leap years.

p=25100=14

Step 2: Find the probability that out of the 2 extra days of the leap year, one is Sunday:

Out of 7days, chances of having Sunday occupying one of those extra two days are 2.

So, p=27

So, the probability of having Sunday on a leap year =14×27

Step 3: Find the probability of having 53 Sundays on a normal year:

A normal year has an extra day.

The probability that Out of 7days, chances of having Sunday occupying that day =17

So, the probability of having Sunday on a normal year =34×17

So, the total probability=14×27+34×17=528

Hence, option (D) is the correct answer.


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