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PDF Editor FAQ

What is probability that two people will share the same birthday, taking into account a leap year possibility?

Based on different assumptions we can arrive at different answers.1. We'll look at the question at a different perspective. People born on a particular day will share the same birthday. We'll assume that number of people born in any given day is same.Number of people born on a particular day= 360,000 (on average)Hence, at any given day 360,000 people are born and will share same birthdays.Total number of people in the world=7.2billion (7,200,000,000)The probability of two people sharing same birthday is same as choosing one in 7.2 billion and then the other should be in set of 360,000 who share same birthday.Hence probability=(7,200,000,000/7,200,000,000)*(359,999/7,200,000,000) which is 0.00052. We'll assume that population growth rate is 0 and average life expectancy is constant.Average life expectancy of humans is 68 years which is 24836 days. Since, the plot of number of persons\age is not known we'll assume that it is constant. Also, the percentage of people whose age is more than 68 years is less than 10% we'll neglect it. Basically the assumption is anybody who is born is supposed to die after 68 years.Hence, if two people have to share the same birthday, then it has to be in a day out of 24836 days.Probability=24836*(1/24836)^2 which is equal to 0.0004023. We'll consider having same birthdays means having same dd\mm and not seeing the year.In this case, Probability is =365*(1/365)^2=0.002739 for a non leap year and 366*(1/366)^2=0.002732 for a leap year.Another interesting fact is if you take a group of 23 people then the probability some pair will have same birthday is 50% and for a group of 75 people it is 99.9% (This is not related to the answer, but its just a cool fact)Birthday problem

What is the probability of guessing one's month and day of birthday correctly?

If I understand your question correctly; I assume by “day” you mean the date in the month, not the day of the week. So your question is equivalent to “What is the probability of guessing someone’s birthday”. That is mm/dd, not the year of course. For simplicity we will assume that birthdays are uniformly distributed across all dates in the year, even though based on data this is not generally true due to the “holiday effect”. Additionally we need to deal with leap year; every 4 years there is a 366th date: Feb. 29.If we ignore those born on Feb. 29 it would be 1/365 ~ 0.2740%If we are smart, we should not guess 2/29, since that birthday is 1/4 as likely. We need to make a minor adjustment in the computation for this.prob(guessing birthday) = 4/(4*365 + 1) = 4/1461 = 1/365.25 ~ 0.2738%

Is Laxmikant Sir's Indian Polity enough for both the prelims and Mains?

M Lakshmikant is bedrock of the civil service examination and it’s more and less sufficient for the need of the examination but in recent times upsc is going extra mile to make the question more versatile, competitive and application based with current affairs acting as cherry 🍒 on the top . So you can add some more resources like -11 ncert political theory for question like freedom, peace , liberty 🗽 etc and it will also help in mainshave a proper understanding and knowledge of current developments like - right to property, Change in NHRC , No of judges in SC etcAdd additional information from your test series and go through new Lakshmikant to understand the various doctrine like -doctrines of eclipse etcfor mains also go through vision mains -365 or ias parliament to have proper clarity and better command over it .If you have time then you can read DD. Basu or. kM Munshi ( but remember Time constraint and revision time required )So Lakshmikant is sufficient enough to cover almost everything but extra resources will give you more cutting edge and you will have more fire power to tackle any type of problems and these additional resources will only take 5–7 days so it’s a win- win situation.

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