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Chapter 5: Q5.4-13E (page 296)

The probability of triplets in human births is approximately 0.001. What is the probability that there will be exactly one set of triplets among 700 births in a large hospital?

Short Answer

Expert verified

0.3476

Step by step solution

01

Given information

The probability of triplets in human births is approximately 0.001. We need to calculate the probability that there will be exactly one set of triplets among 700 births in a large hospital.

02

Calculating the required probability

Let X denotes the number of triplets in the sample. Then X follows Binomial distribution with parameters n=700 and p=0.001. Since n is large and p is small, we can use the Poisson approximation to the Binomial distribution.

Now,

\(\begin{array}{l}P\left( {X = x} \right) = \frac{{{e^{ - \lambda }}{\lambda ^x}}}{{x!}}\\P\left( {X = 1} \right) = \frac{{{e^{ - 0.7}}{{\left( {0.7} \right)}^1}}}{{1!}}\,\,{\rm{as}}\,\lambda = np = 700 \times 0.001 = 0.7\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.3476\end{array}\)

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