Question: In the Case Study described at the beginning of this chapter you were told that if birth dates are random and independent, the chance that three children share the same birth date is about 7.5 in a million.
1. Go to the most recent Statistical Abstract (online at www.census.gov/ compendia/statab/) and look under "Population," "Households and Families," "Families by Number of Own Children under 18 Years Old." How many families in the United States have at least three children under 18 years old?
2. For the time being, assume that the families you found in the previous question all have exactly three children. If the chance that three children share the same birth date is about 7.5 in a million, what proportion of the families in the previous question will have three who share the same birth date? About how many of these families might you expect to have all three children with the same birth date?
3. Do you think that the number of families in which there are three children who share the same birth date is much larger than the number you estimated in the previous question? You may want to consider the fact that not all the families have exactly three children, that the number of families does not include those with children over the age of 18, and that parents might intentionally try to conceive children with the same birth date.
4. Write a paragraph discussing whether the "surprising" coincidence described in the Case Study that began this chapter is as surprising as it might first appear