# Math Help - Poisson approximation

1. ## Poisson approximation

Question : If the probability that an individual suffers from a bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals
i) exactly 3 individuals will suffer a bad reaction,
ii) more that 2 individuals will suffer a bad reaction by using Poisson approximation. Also give exact probabilities( you need not simplify the expression)

2. Originally Posted by zorro
Question : If the probability that an individual suffers from a bad reaction from an injection of a given serum is 0.001, determine the probability that out of 2000 individuals
i) exactly 3 individuals will suffer a bad reaction,
ii) more that 2 individuals will suffer a bad reaction by using Poisson approximation. Also give exact probabilities( you need not simplify the expression)
What have you tried? Where are you stuck? What thoughts do you have? Do you know what the Poisson approximation is an approximation to? Have you looked up the Poisson approximation in your classnotes or textbook?

3. ## Please check if it is correct or no

Originally Posted by mr fantastic
What have you tried? Where are you stuck? What thoughts do you have? Do you know what the Poisson approximation is an approximation to? Have you looked up the Poisson approximation in your classnotes or textbook?
i)
$p(x, \lambda)$ = $\frac{\lambda^{-x}}{x!} . e^{- \lambda}$

$\lambda$ = $n \theta$

$\lambda \ = \ 2$

$p(3, \lambda)$= $\frac{e^{-2}}{3!} . 2^3$ = $\frac{4 e^{-2}}{3}$ ...............Is that correct ?

ii) P(X>2, \lambda) = ___________............I dont know what to do ?

4. For the second one, add up the probabilities for 0 to 2 and subtract from 1.

The first one looks OK.