Question

According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per $1,000$babies in a healthy baby nursery. The number climbs to an average of $30$per $1,000$babies in an intensive care nursery.

Suppose that $1,000$babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies were born deaf.

Short answer

The probability that two children were born deaf is$0.27094$.

Step-by-step solution

Given information

The average number of babies born with significant hearing loss in a healthy baby nursery is approximately two per $1000$babies.

Explanation

$P(X=x)==C_x^n\times p^x\times {\left(1-p\right)}^{n-x}$

$n=1000$,$p=0.002$,$x=2$

$$\begin{gathered} P\left(\text{thatexactlytwobabieswereborndeaf}\right)=C_2^{2000}\times {\left(\frac{2}{1000}\right)}^2\times {\left(\frac{998}{1000}\right)}^{998} \\ P\left(\text{thatexactlytwobabieswereborndeaf}\right)=0.271 \end{gathered}$$

The probability that exactly two babies were born deaf is $0.271$