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 = Cases where we have Tuesday = {(Mon, Tues), (Tues, Wed)} Therefore, Probability that a leap year will contain 53 Tuesdays = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑜𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑐𝑎𝑠𝑒𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑠𝑒𝑠) = 𝟐/𝟕

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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