First slide

Random variable and probability distribution

Question

The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals more than 2 suffer a bad reaction is

Moderate

A

$\frac{5}{e^{2}}$
B

$1 - \frac{5}{e^{2}}$
C

$1 - \frac{4}{e^{2}}$
D

$\frac{4}{e^{2}}$

Solution

$p = 0.001, n = 2000$
$λ = n p = 2$

$P (X > 2) = 1 - [P (X = 0) + P (X = 1) + P (X = 2)]$

= $1 - [1 + \frac{2^{1}}{1!} + \frac{2^{2}}{2!}] e^{- 2}$

= $1 - \frac{5}{e^{2}}$

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