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Question

# If a leap-leap year selected at random, the chance that it will contain 53 Sundays is

A
37
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B
17
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C
1367
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D
None of these
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Solution

## The correct option is A 37A leap-leap year has 367 days i.e. 52 complete week and three days more. These three days will be three consecutive days of a week. A leap-leap year will have 53 Sundays if out of the three consecutive days of a week selected at random one is a Sunday.Let S be the sample space and E be the event that out of the three consecutive days of a week one is Sunday, thenS= {(Sunday,Monday,Tuesday,(Monday,Tuesday,Wednesday),(Tuesday,Wednesday,Thursday),(Wednesday,Thursday,Friday),(Thursday,Friday,Saturday),(Friday,Saturday,Sunday),(Saturday,Sunday,Monday)}∴n(S)=7and E={(Sunday,Monday,Tuesday),((Friday,Saturday,Sunday),(Saturday,Sunday,Monday)}∴n(E)=3Hence, Required probability P(E)=n(E)n(S)=37

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