People are surprised to find that it is not all that uncommon for two people in a group of 20 to 30 people to have the same birthday. We will learn how to find that probability in a later chapter. For now, consider the probability of finding two people who have birthdays in the same month. Make the simplifying assumption that the probability that a randomly selected person will have a birth day in any given month is 1/12. Suppose there are three people in a room and you consecutively ask them their birthdays. Your goal, following parts (a–d), is to determine the probability that at least two of them were born in the same calendar month.
a. What is the probability that the second person you ask will not have the same birth month as the first person?
b. Assuming the first and second persons have different birth months, what is the probability that the third person will have yet a different birth month?
c. Explain what it would mean about overlap among the three birth months if the outcomes in part (a) and part (b) both happened. What is the probability that the outcomes in part (a) and part (b) will both happen?
d. Explain what it would mean about overlap among the three birth months if the outcomes in part (a) and part (b) did not both happen. What is the probability of that occurring?