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## Main Question or Discussion Point

Hello PF

This might be a fairly simple question to most of you, but I was given this problem (don't worry, I already solved it just wondering about something)

Suppose the probability of suffering a side effect of a certain flu vaccine is 0.005. If 1000 persons are inoculate, find the approximate probability that

(a) at most 1 person suffers, (b) 4,5, or 6 persons suffer.

I already solved it, but this problem is in the chapter on the Poisson distribution. Unfortunately my teacher didn't cover this distribution in detail, but when I first looked at the problem it look like a typical Binomial distribution problem? I later figured out I was supposed to approximate with the Poisson distribution.

Why would we use an approximation for the Binomial when we could just apply it, and under what circumstances am I allowed to make this approximation in the first place?

This might be a fairly simple question to most of you, but I was given this problem (don't worry, I already solved it just wondering about something)

Suppose the probability of suffering a side effect of a certain flu vaccine is 0.005. If 1000 persons are inoculate, find the approximate probability that

(a) at most 1 person suffers, (b) 4,5, or 6 persons suffer.

I already solved it, but this problem is in the chapter on the Poisson distribution. Unfortunately my teacher didn't cover this distribution in detail, but when I first looked at the problem it look like a typical Binomial distribution problem? I later figured out I was supposed to approximate with the Poisson distribution.

Why would we use an approximation for the Binomial when we could just apply it, and under what circumstances am I allowed to make this approximation in the first place?