Lesson 4-6Probability 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 23-41 and odds 47-59