Chapter 2: Rational Numbers

2.7Probability of Compound Events

Independent Events• Events that do not influence each other

• Example:– Drawing a card, then putting it back before drawing

another

• Probability of Two Independent Events:– If A and B are independent events:

)()()( BPAPAandBP

Example 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?

Example 1a

• 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?

Example 2• In a word game, you choose a tile at random from a

bag containing the letter tiles I, U, I, A, O, O, O, E, A, U, A, O, A, E, 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?

Example 2a

• In a word game, you choose a tile at random from a bag containing the letter tiles I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Find the probability that you will choose at random a U and then an I after replacing the first tile.

Probability of Two Dependent Events

• Dependent events– Events that influence each other

• Probability:

)()()( BafterAPAPAthenBP

Example 3

• Suppose you choose a tile at random from the letter tiles I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Without replacing the tile, you select a second tile. What is the probability that you will choose an A and then an E?

Example 3a

• Suppose you choose a tile at random from the letter tiles I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Find the probability that you will choose at random a U and then an O without replacing the first tile.

Example 4• 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?

Example 4a• 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 junior are chosen?

Example 4b• 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 junior and then a sophomore are chosen?

Homework

• P. 104

• 2-28 even, 36-40 even