Q81 / 160 · TS EAMCET 2018 (05 May Shift 1) · Mathematics

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

  • A
    $\frac{7}{2 e^3}$
  • Correct answer
    B
    $\frac{9}{2 e^3}$
  • C
    $\frac{7}{e^3}$
  • D
    $\frac{9}{e^3}$

Solution

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, $$ P(X=x)=\frac{e^{-\mu}, \mu^x}{x !} P(X=2)=\frac{e^{-3} \cdot 3^2}{2 !}=\frac{9}{2 e^3} $$

Hence, the correct answer is option: 'B'.

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