Question

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

Answer 1

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;

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

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 = $\frac{11}{2000}$ = 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)  

                                  =  $1- \binom{1200}{0} \times 0.0055^{0} \times (1-0.0055)^{1200-0}$

                                  =  $1- (1 \times 1 \times 0.9945^{1200})$

                                  =  0.9987 or 99.87%

Hence, the required probability is 99.87%.