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If the probability of a bad reaction from a vaccination is 0.01 , then the probability that exactly two out of 300 people will get bad reaction is
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Verified Answer
The correct answer is:
$\frac{9}{2 e^3}$
Probability of a bad reaction from a vaccination is 0.01
$P=0.01$ and $n=300$
Here, binomial distribution is applicable with poission approximation
mean $(\mu)=n p=0.01 \times 300=3$
Apply poission distribution,
$$
P(X=x)=\frac{e^{-\mu}, \mu^x}{x !} P(X=2)=\frac{e^{-3} \cdot 3^2}{2 !}=\frac{9}{2 e^3}
$$
$P=0.01$ and $n=300$
Here, binomial distribution is applicable with poission approximation
mean $(\mu)=n p=0.01 \times 300=3$
Apply poission distribution,
$$
P(X=x)=\frac{e^{-\mu}, \mu^x}{x !} P(X=2)=\frac{e^{-3} \cdot 3^2}{2 !}=\frac{9}{2 e^3}
$$
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