Misc 8 - In leap year, what is chance it will contain 53 Tuesdays - Miscellaneous

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  1. Chapter 13 Class 12 Probability
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Misc 8 If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays? A leap year has 366 days Dividing by 7, Number of weeks in a leap year = 366﷮7﷯ = 52 2﷮7﷯ Thus, a leap year has 52 weeks and 2 days extra. Hence, a leap year will have 52 Tuesdays for sure Now, the 2 extra days can be {(Monday, Tuesday), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun), (Sun, Mon)} Favorable cases = {(Mon, Tues), (Tues, Wed)} ∴ Probability that a leap year will contain 53 Tuesdays = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑜𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑐𝑎𝑠𝑒𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠﷯ = 𝟐﷮𝟕﷯

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