Answer :
Answer:
Probability that one or more people in Arbalest got a cold is 0.9987.
Step-by-step explanation:
We are given that according to a report, 11 people got colds for every 2000 people.
There are 1200 people in the town of Arbalest.
The above situation can be represented through binomial distribution;
[tex]P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 1200 people
r = number of success = one or more people got a cold
p = probability of success which in our question is probability
that people got colds, i.e; p = [tex]\frac{11}{2000}[/tex] = 0.55%
Let X = Number of people in Arbalest who got a cold
So, X ~ Binom(n = 1200 , p = 0.0055)
Now, Probability that one or more people in Arbalest got a cold is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1- \binom{1200}{0} \times 0.0055^{0} \times (1-0.0055)^{1200-0}[/tex]
= [tex]1- (1 \times 1 \times 0.9945^{1200})[/tex]
= 0.9987 or 99.87%
Hence, the required probability is 99.87%.