Almost Friday! Warm-Up… Quickwrite… What is the most mixed grade levels class you have ever taken? How did it feel to study with mixed grades? Ex: “The most mixed class I have ever taken is _______. It felt __________because _______________________.”

Compare and Explain… your Warm-Up starting with Student #1 (1 min) b) 0.04 a) 0.56 b) 0.63

Round Robin… starting with the student who has the earliest birth month at your table (1 min) What is the most mixed grade levels class you have ever taken? How did it feel to study with mixed grades? Ex: “The most mixed class I have ever taken is _______. It felt __________because _______________________.”

Homework

Addition rules

Two Events Happening Together One of the multiplication rules can be used any time we are trying to find the probability of two events happening together Pictorially, we are looking for the probability of the shaded region The Event A and B

One Event OR Another Another way to combine events is to consider the possibility of one event OR another occurring For instance, if a sports car saleswoman gets an extra bonus if she sells a convertible or a car with leather upholstery, she is interested in the probability that you will buy a car that is a convertible or that has leather upholstery

The Event A or B

Example: Events Combined with OR Consider an introductory statistics class with 31 students The students range from freshmen through seniors; some students are male and some are female Sample Space for Statistics Class

Example Suppose we select one student at random from the class How do we find the probability that the student is either a freshman or a sophomore? Since there are 15 freshmen out of 31 students, P (freshmen) = Since there are 8 sophomores out of 31 students, P (sophomore) = P (freshmen or sophomore) =

Example If we select one student at random from the class, what is the probability that the student is either a male or a sophomore?

Example If we simply add P (sophomore) and P (male), we’re including P (sophomore and male) twice in the sum To compensate for this double summing, we simply subtract P (sophomore and male) from the sum Therefore, P (sophomore or male) = P (sophomore) + P (male) – P (sophomore and male)

Addition Rules

Example: Mutually Exclusive Events We are playing Monopoly and on our next move we need to throw a sum bigger than 8 on the two dice in order to land on our own property and pass Go What is the probability that we will roll a sum bigger than 8? Solution: The largest sum that can come up is 12 and the only sums larger than 8 are 9, 10, 11, and 12 These outcomes are mutually exclusive, since only one of these sums can possibly occur on one throw of the dice

Example The probability of throwing more than 8 is the same as P(9 or 10 or 11 or 12) Since the events are mutually exclusive, P(9 or 10 or 11 or 12) = P(9) + P(10) + P(11) + P(12)

Practice Suppose an employee is selected at random from the group of 140