A group of 30 people is selected at random. What is the probability that at least 2 of them will have the same birthday?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A group of 30 people is selected at random. What is the
Given : A group of 30 people is selected at random.
Question : What is the probability that at least 2 of them will have the same birthday?
Probability ( at least 2 people share the same birthday ) is also can be written as :
Probability ( at least 2 people share the same birthday ) = 1 - P( no two people share the same birthday)
First compute the probability that two people share different birthday .
Let us say that , first person we pick has a birthday and it can be on any day of the year i.e. any of the 365 days .
So it will be :
The next person, person 2, can have a birthday on any day of the year except for the one that person 1 has birthday on a particular day ,
So it will be :
Simultaneously , two of them having different birthdays is :
x
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