Probability of event modelled by poisson happening twice, consecutively

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    Poisson Probability
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SUMMARY

The discussion centers on calculating the probability of receiving at least three telephone calls in two consecutive one-minute intervals, modeled by a Poisson distribution with a mean of 3.5. The correct approach involves determining the probability of receiving at least three calls in a single interval, denoted as P(≥3), and then squaring this probability to account for the two successive intervals. This results in the formula P(≥3) x P(≥3) to find the overall probability for both intervals.

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This discussion is beneficial for statisticians, data analysts, and students studying probability theory, particularly those interested in applying Poisson distribution to real-world scenarios.

cmkluza
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I'm not great at statistics, so I don't know where to start with this problem. It is stated as follows:

The number of telephone calls, T, received each minute can be modeled by a Poisson distribution with a mean of 3.5.

Find the probability that at least three telephone calls are received in each of two successive one-minute intervals.

So, I understand we have T ~ Po(3.5), and using a calculator or formula, I could easily identify the probability of having at least three telephone calls, but I don't understand what to do about that two successive part. Been thinking on this one for a while, but I'm at a loss as to what to do. Can anyone give me any suggestions on how to think about this to arrive at an answer?
 
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You could multiply the probability of atleast 3 successive calls twice i.e P($$\ge$$ 3 phone calls) x P($$\ge$$ 3 phone calls), since our event gets completed only if we consider both of it's elements(in this case, the number of calls in two successive minutes).

This is just my suggestion as I, myself, am certainly not an ace in the area of statistics.
 

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