InterviewSolution
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InterviewSolution
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The probability that in a year of `22nd` centurychosen at random, there will be 53 Sundays isA. `(3)/(28)`B. `(2)/(28)`C. `(7)/(28)`D. `(5)/(28)` |
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Answer» Correct Answer - D In the 22nd century there are 25 leap years viz. 2100, 2104,.., 2196 and 75 non-leap years. Consider the following events : `E_(1)` = Selecting a leap year 22nd century `E_(2)`= Selecting a non-leap year from 22nd century A=There are 53 Sundays in a year of 22nd century We have, `P(E_(1))=(25)/(100), P(E_(2))=(75)/(100)` `P(A//E_(1))=(2)/(7) " and " P(A//E_(2))=(1)/(7)` Required probability =P(A) `=P((A cap E_(1)) cup (A cap E_(2)))` `=P(A cap E_(1))+P(A cap E_(2))` `=P(E_(1))P(A//E_(1))+P(E_(2))P(A//E_(2))` `=(25)/(100)xx(2)/(7)+(75)/(100)xx(1)/(7)=(5)/(28)` |
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