1. 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)

2. 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)