Question: On October 5, 2007, a Marysville, Ohio, woman gave birth to her third child. The date of birth for this child was the same as for her two previous children. The Associated Press picked up the story and it was run in newspapers around the country as an amazing coincidence. If births dates are random and independent, a probabilist can show that the chance that three children share the same birth date is about 7.5 in a million. The rarity of the event is what made the story newsworthy.
Just how amazing is this event? In this chapter we will learn how to interpret probabilities like 7.5 in a million. By the end of this chapter you will be able to assess coincidences like having three children who share the same birth date. Are they as surprising as they seem?