Lesson 4-6 Probability of Compound Events Objectives: To find the probability of independent and dependent events.

Why should we learn this? One real-world connection is to consider how probability is used in a game, as in Example 3.

INDEPENDENT EVENTS Independent events – events that do not influence one another RULE: If A and B are independent events, P(A and B) = P(A) P(B)

Example 1, page 220 Suppose you roll a red number cube and a blue number cube. What is the probability that you will roll a 5 on the red cube and a 1 or 2 on the blue cube? Answer: 1/18

Example 2, page 220 In a word game, you choose a tile from a bag containing the letter tiles I, U, I, A, O, O, E, A, O, U, O, A, E, A, E. You replace the first tile in the bag and then choose again. What is the probability that you will choose an A and then an E? Find the probability of picking a U and then an I after replacing the first tile. Answer: 4/225

DEPENDENT EVENTS Dependent events – events that influence each other RULE: IF A and B are dependent events, P(A then B) = P(A) P(B after A)

Example 3, page 221 Suppose you choose a tile from the letter tiles shown in example 2 (I, U, I, A, O, O, E, A, O, U, O, A, E, A, E). Without replacing the tile, you select a second tile. What is the probability that you will choose an A and then and E? Find the probability that you will choose a U and then an O without replacing the first tile. Answer: 4/105

Example 4, page 221 Suppose a teacher must select 2 high school students to represent their school conference. The teacher randomly picks names from a hat that contains the names of 3 freshmen, 2 sophomores, 4 juniors, and 4 seniors. What is the probability that a sophomore and then a freshman are chosen? 4a) What is the probability that the teacher chooses a sophomore and then a junior? B) a junior and then a sophomore?

Example 4c C) Does the probability of choosing without replacement change if the order of the events is reversed? Explain.

SUMMARY Probability of Independent Events = P(A) P(B) Probability of Dependent Events = P(A) P(B after A)

ASSIGNMENT #4-6, page 222, 1-22 all, odds and odds 47-59