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In leap year, what is chance it will contain 53 Tuesdays (Probability)

Misc 8 - Chapter 13 Class 12 Probability - Part 2


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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.