Please copy your homework into your assignment book BEFORE THE BELL RINGS Please copy your homework into your assignment book Have your homework out to review

Warm Up Find the theoretical probability of each outcome 1. rolling a 6 on a number cube. 2. rolling an odd number on a number cube. 3. flipping two coins and both landing heads up

Thursday, December 15, 2016 Warm-up Last Minute Questions? Probability Test Independent and Dependent Events Reading Homework: Finish Independent and Dependent Events Reading

Independent and Dependent Event Algebra 1 Independent and Dependent Event

Objectives Find the probability of independent events. Find the probability of dependent events.

Definitions Events are independent events if the occurrence of one event does not affect the probability of the other. Events are dependent events if the occurrence of one event does affect the probability of the other.

Classifying Events as Independent or Dependent Tell whether each set of events is independent or dependent. Explain you answer. A. You select a card from a standard deck of cards and hold it. A friend selects another card from the same deck. B. You flip a coin and it lands heads up. You flip the same coin and it lands heads up again.

Check It Out! Tell whether each set of events is independent or dependent. Explain you answer. a. A number cube lands showing an odd number. It is rolled a second time and lands showing a 6. b. One student in your class is chosen for a project. Then another student in the class is chosen.

Tree Diagram Suppose an experiment involves flipping two fair coins. The sample space of outcomes is shown by the tree diagram. Determine the theoretical probability of both coins landing heads up.

Independent Probabilites Now look back at the separate theoretical probabilities of each coin landing heads up. The theoretical probability in each case is . The product of these two probabilities is the same probability shown by the tree diagram.

Independent Probabilities

Finding the Probability of Independent Events An experiment consists of randomly selecting a marble from a bag, replacing it, and then selecting another marble. The bag contains 3 red marbles and 12 green marbles. What is the probability of selecting a red marble and then a green marble?

Example A coin is flipped 4 times. What is the probability of flipping 4 heads in a row.

Check It Out! An experiment consists of spinning the spinner twice. What is the probability of spinning two odd numbers?

Dependent Probabilities Suppose an experiment involves drawing marbles from a bag. Determine the theoretical probability of drawing a red marble and then drawing a second red marble without replacing the first one.

Dependent Probabilities To determine the probability of two dependent events, multiply the probability of the first event times the probability of the second event after the first event has occurred.

Application A snack cart has 6 bags of pretzels and 10 bags of chips. Grant selects a bag at random, and then Iris selects a bag at random. What is the probability that Grant will select a bag of pretzels and Iris will select a bag of chips?

Check It Out! A bag has 10 red marbles, 12 white marbles, and 8 blue marbles. Two marbles are randomly drawn from the bag. What is the probability of drawing a blue marble and then a red marble?

Warm-Up 1. Eight cards are numbered from 1 to 8 and placed in a box. One card is selected at random and not replaced. Another card is randomly selected. What is the probability that both cards are greater than 5? 2. An experiment consists of randomly selecting a marble from a bag, replacing it, and then selecting another marble. The bag contains 3 yellow marbles and 2 white marbles. What is the probability of selecting a white marble and then a yellow marble?`