If A and B are independent events, P (A and B) = P (A) P (B) Probability of Compound Events Independent Events: 1. Suppose you roll a red number cube and a blue number cube. What is the probability that you will roll a 3 on the red cube and an even number on the blue cube? 2. In a word game, you choose a tile from a bag containing the letters U I I A O O E A O O U A A E E. You replace the first tile in the bad and then choose again. What is the probability that you will choose an A and then an E? 3. (See example 2 above) Find the probability of picking a U and then an I after replacing the first tile. Probability of Two Independent Events Events that do not influence one another If A and B are independent events, P (A and B) = P (A) P (B)

If A and B are dependent events, P (A then B) = P (A) P (B after A) Probability of Compound Events Dependent Events: 4. Suppose you choose a tile from the letter from the letter tiles shown in example 2 above. Without replacing the tile, you select a second tile. What is the probability that you will choose an A and then an E? 5. Suppose a teacher must select 2 high school students to represent their school at a 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? Probability of Two Dependent Events Events that influence each other. The occurrence of one event affects the probability of a second event. If A and B are dependent events, P (A then B) = P (A) P (B after A)