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Kelly goes to a conference where there are 700 other people. Kelly discovers that 6 other...

Kelly goes to a conference where there are 700 other people. Kelly discovers that 6 other people have her same birthday.

Estimate the probability that six other people have the same birthday. Does the poisson approximation work here? Explain.

math   Statistics-And-Probability   
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Answer #1

Poisson distribution is used to find the probability of a number of events occurring in a time interval given the average number of events occurring per unit time.

Since here, no time constraint is mentioned. Hence, we cannot make it a Poisson distribution problem.

Rather, it is a binomial distribution problem with success probability p is given by

Probability that one other person out of 700 has same birthday as Kelly = 1/365 =0.00274

Probability of failure = q = 1 - p

Also, number of trials = n = 700

Number of success = x = 6

So, the probability that exactly 6 other people have same birthday as Kelly

= P(X = 6)

= 700C6 × (1/365)6 ×(364/365)700 - 6

= 0.01008

so, there is 1.008 % chance that 6 other people at conference will have same birthday as Kelly.

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