Question

2. Suppose that the probabilty that an individual suffers a bad reaction from a vaccine is 0.001.
Determine the probabilty that out of 2000 individuals:
• Exactly 3 people have a reaction
• More than 2 people have a reaction

Answer 1

Here, n = 2000, p = 0.001, (1 - p) = 0.999 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 3)
P(X = 3) = 2000C3 * 0.001^3 * 0.999^1997
P(X = 3) = 0.1805
0

Here, n = 2000, p = 0.001, (1 - p) = 0.999 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X > 2).
P(X <= 2) = (2000C0 * 0.001^0 * 0.999^2000) + (2000C1 * 0.001^1 * 0.999^1999) + (2000C2 * 0.001^2 * 0.999^1998)
P(X <= 2) = 0.1352 + 0.2707 + 0.2708
P(X <= 2) = 0.6767

P(x> 2)= 1 - P(x< =2)
= 1 - 0.6767
= 0.3233