The probability that in a year of 22nd century chosen at random, there will be 53 sundays is

The probability that in a year of 22nd century chosen at random, there will be 53 sundays is

  1. A

    328

  2. B

    228

  3. C

    728

  4. D

    528

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    Solution:

    In the 22nd century there are 25 leap years viz. 

    2100, 2104,…,2196 and 75 non- leap years.

    Consider the following events : 

           E1 = Selecting a leap year from 22nd century

          E2 = Selecting a non-leap year from 22nd century

          A = There are 53 Sundays in a year of 22nd century 

     We have, 

       PE1=25100,   PE2=75100

    PA/E1=27 and PA/E2=17

    Required probability =P(A)=PAE1AE2=PAE1+PAE2=PE1PA/E1+PE2PA/E2=25100×27+75100×17=528 

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