Question

Refer to the following information on births in the United States over a given period of time: $$ \begin{array}{lr} \text { Type of Birth } & \text { Number of Births } \\ \hline \text { Single birth } & 41,500,000 \\ \text { Twins } & 500,000 \\ \text { Triplets } & 5000 \\ \text { Quadruplets } & 100 \\ & \\ \hline \end{array} $$ Use this information to approximate the probability that a randomly selected pregnant woman who reaches full term a. Delivers twins b. Delivers quadruplets c. Gives birth to more than a single child

Short answer

The approximate probabilities are \(P(Twins) = 0.0119\), \(P(Quadruplets) = 0.00000238\), and \(P(More than one child) = 0.0120\)

Step-by-step solution

Calculate Total Number of Births

First, calculate the total number of births. This will be the sum of single births, twins, triplets, and quadruplets, i.e., \(41,500,000 + 500,000 + 5,000 + 100 = 42,005,100.\)

Calculate Probabilities

The probability can be calculated as the ratio of the number of such births to the total number of births. For example, the probability of having twins is calculated as \(P(twins) = \frac{Number\:of\:Twins}{Total\:Number\:of\:Births} = \frac{500,000}{42,005,100}. Similarly, we calculate the probabilities for quadruplets and for giving birth to more than a single child.

Calculate Probability of more than one child

The probability of giving birth to more than one child involves twins, triplets and quadruplets. Therefore, calculate the sum of twins, triplets, and quadruplets and divide by total births i.e., \(P(more\:than\:one\:child)=\frac{Number\:of\:Twins+Number\:of\:Triplets+Number\:of\:Quadruplets}{Total\:Number\:of\:Births}=\frac{500,000+5,000+100}{42,005,100}\).