Simulations are really useful to see ahead what happen in a specific phenomenon. In genetic is really important to explore in advance the gender of the new born when there are records of genetic problems in the family. For example in a family with antecedents of hemophilia (congenital tendency to uncontrolled bleeding), the couple could be interested in knowing the probabilities of having a male in a two-child family. This exploration is really crucial since hemophilia usually affects males and is transmitted from mother to son.

Let us to construct the simulation

To make the simulation we have to take into account that the probabilities of being born male or female are slightly similar.

We can use either coins, dice or spinners to make the simulation.

Explain how to use a coin to simulate the birth of one child . What does a head represent? what does a tail represent? what assumptions are you making?

Explain how to use a coin to simulate the births of two children in the family.

To be sure you have a reasonable estimate, it is necessary to run many trial. Conduct 300 trial simulating a two-child families

Type of family	Frequency
two females
older female and younger male
older male and younger female
two males
Total number of trial	300

Use the table of frequency to estimate the probability that the family has at least a male child

Estimate the probability that a family with two children will have at least a boy using a method other than simulation. Compare your results with those got in part 4.

Do the four types of families seem to be equally likely?

Use the spreadsheet to make a histogram with your gathered data.

On the histogram locate the median, the mean and the mode.

Describe the form of your distribution.

What is the largest family size?

References

Coxford A. F. et al. (1997) Contemporary Mathematics in Context: a unified approach. . Course 1 Part B. Everyday Learning Corporation: Chicago Illinois

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