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Question

# The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is

A
713
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B
223
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C
37
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D
None of these
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Solution

## The correct option is C 37Total number of days in a leap year is 366.It will contain 52 weeks and 2 days.These two days can beS={(Sun,Mon);(Mon,Tues);(Tues,Wed);(Wed,Thurs);(Thurs,Fri);(Fri,Sat);(Sat,Sun)}Therefore n(S)=7Let A be the event of getting 53 sundays.Therefore A={(Sun,Mon);(Sat,Sun)}For 53 Sundays , probability is P(A)=27Let B be the event of getting 53 mondays.Therefore B={(Sun,Mon);(Mon,Tues)}For 53 Mondays , probability is P(B)=27=27This includes one ways where sunday and monday simultaneously Occur(i.e) A∩B={Sun,Mon}Probability for this is P(A∩B)=17.=17Hence required probability that a leap year selected at random contain 53 sundays or 53 mondays is P(A∪B)=P(A)+P(B)−P(A∩B) =27+27−17=2+2−17Therefore the required probability is 37

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