Question

According to a report, 11 people got colds for every 2000 people.

There are 1200 people in the town of Arbalest. What is the
probability that one or more people in Arbalest got a cold?
_ % (Round your answer to the nearest hundredth)

Answer 1

Probability that one or more people in Arbalest got a cold is 0.9987.

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;

`P(X =r) = \binom{n}{r} * p^(r) * (1-p)^(n-r);x=0,1,2,3,......`

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 =
`(11)/(2000)` = 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
`\geq` 1)

P(X
`\geq` 1) = 1 - P(X = 0)

=
`1- \binom{1200}{0} * 0.0055^(0) * (1-0.0055)^(1200-0)`

=
`1- (1 * 1 * 0.9945^(1200))`

= 0.9987 or 99.87%

Hence, the required probability is 99.87%.