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 head up

Independent and Dependent Events 10-7 Holt Algebra 1

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.

Example 1: 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. Dependent; your friend cannot pick the card you picked and has fewer cards to choose from. B. You flip a coin and it lands heads up. You flip the same coin and it lands heads up again. Independent; the result of the first toss does not affect the sample space for the second toss.

Check It Out! Example 1 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. Independent; the result of rolling the number cube the 1st time does not affect the result of the 2nd roll. b. One student in your class is chosen for a project. Then another student in the class is chosen. Dependent; choosing the 1st student leaves fewer students to choose from the 2nd time.

Suppose an experiment involves flipping two fair coins 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.

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? Because the first marble is replaced after it is selected, the sample space for each selection is the same. The events are independent. P(red, green) = P(red)  P(green)

Example 2B: Finding the Probability of Independent Events A coin is flipped 4 times. What is the probability of flipping 4 heads in a row. Because each flip of the coin has an equal probability of landing heads up, or a tails, the sample space for each flip is the same. The events are independent. P(h, h, h, h) = P(h) • P(h) • P(h) • P(h) The probability of landing heads up is with each event.

Example 3: 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?

P(pretzel and chip) = P(pretzel) P(chip after pretzel) Example 3 Continued P(pretzel and chip) = P(pretzel) P(chip after pretzel) • Grant selects one of 6 bags of pretzels from 16 total bags. Then Iris selects one of 10 bags of chips from 15 total bags. The probability that Grant selects a bag of pretzels and Iris selects a bag of chips is .

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Lesson Quiz: Part I Tell whether each set of events is independent or dependent. Explain your answer. 1. flipping two different coins and each coin landing showing heads Independent; the flip of the first coin does not affect the sample space for the flip of the second coin. 2. drawing a red card from a standard deck of cards and not replacing it; then drawing a black card from the same deck of cards Dependent; there are fewer cards to choose from when drawing the black card.

Lesson Quiz: Part II 3. 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? 4. 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?

Lesson Quiz: Part III 5. A number cube is rolled two times. What is the probability of rolling an even number first and then a number less than 3?