# Question: People are surprised to find that it is not all

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?

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?

**View Solution:**## Answer to relevant Questions

A restaurant server knows that the probability that a customer will order coffee is .30, the probability that a customer will order a diet soda is .40, and the probability that a customer will request a glass of water is ...Suppose the probability that you get an A in any class you take is .3, and the probability that you get a B is .7. To construct a GPA, an A is worth 4.0, and a B is worth 3.0. What is the expected value for your GPA? Would ...Suppose your are able to obtain a list of the names of everyone in your school and you want to determine the probability that someone randomly selected from your school has the same first name as you. a. Assuming you had the ...The scenario in this exercise is similar to the one in Exercise 7, except the class size is smaller. Suppose that there are 15 students in your class. Each day the teacher randomly selects one student to show the others how ...As a promotion, a cereal brand is offering a prize in each box, and there are four possible prizes. You would like to collect all four prizes, but you only plan to buy six boxes of the cereal before the promotion ends. ...Post your question