1. How Many Outcomes Are There for Rolling a Die?

11-3 Probability of Multiple Events

Warm Up!

1. How many outcomes are there for rolling a die?

2. How many outcomes are there for tossing a coin?

3. How many outcomes are there for rolling a die and then tossing a coin?

4. Does the outcome from rolling a die affect the outcome of tossing a coin? Explain.

Vocabulary

Compound Event – Probabilities of two or more things happening at once.

Independent Events – When the outcome of one event does not affect the probability of second event, the two events are independent.

Dependent Events – Two events are dependent if the occurrence of one event affects the probability of the second event.

Example 1: Tell whether each event is independent or dependent.

a.) Earning grades on your tests and earning your final semester grade.

b.) Selecting a red apple and then a green apple from a bag of 6 red and 4 green apples, if no apples are returned to the bag.

c.) Selecting a red apple and then a green apple from a bag of 6 red and 4 green apples, if the first apple is returned to the bag before the next selection.

d.) Flipping a coin and pulling a card from a deck of cards.

Example2: Suppose you toss a coin and roll a die. Find the probability of getting heads on the coin and ‘5’ on the die.

Example3: Suppose you spin a spinner with the numbers 1, 2, 3, and 4, and pick a card from a standard deck. Find the probability of spinning a ‘4’ and choosing a face card.

Example4: A bag contains 3 red marbles and 5 blue marbles. One marble is chosen at random and then replaced. A second marble is drawn. Find P(red, then blue).

Example5: A bag contains three red marbles and five blue marbles. One marble is chosen at random and is not replaced. A second marble is drawn. Find P(red, then blue).

Example 6: There are five discs in a CD player. Disc 1 has 8 songs, disc 2 has 10 songs, disc 3 has 13 songs, disc 4 has 9 songs, and disc 5 has 10 songs. The player has a “random” button that selects songs at random and does not repeat until all songs are played. What is the probability that the first song is selected from disc 3 and then second song is selected from disc 4?

Example7: Two cards are drawn from a standard deck. The first card is not returned to the deck before the second draw. Find P(face, then face).

Homework: pp. 708 – 709 =>9 – 15, 22 – 26, 31 – 34

Algebra 2: Lesson 11-3 Probability of Multiple EventsPage 1