31
Holt Algebra 1 10-7 Independent and Dependent Events 10-7 Independent and Dependent Events Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz
| Date post: | 26-Dec-2015 |
| Category: |
Documents |
| Upload: | winfred-lee |
| View: | 264 times |
| Download: | 5 times |
Holt Algebra 1
10-7 Independent and Dependent Events10-7 Independent and Dependent Events
Holt Algebra 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt Algebra 1
10-7 Independent and Dependent Events
Warm UpFind 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
Holt Algebra 1
10-7 Independent and Dependent Events
Find the probability of independent events.
Find the probability of dependent events.
Objectives
Holt Algebra 1
10-7 Independent and Dependent Events
independent eventsdependent events
Vocabulary
Holt Algebra 1
10-7 Independent and Dependent Events
Adam’s teacher gives the class two list of titles and asks each student to choose two of them to read. Adam can choose one title from each list or two titles from the same list.
Holt Algebra 1
10-7 Independent and Dependent Events
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.
Holt Algebra 1
10-7 Independent and Dependent Events
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.
Holt Algebra 1
10-7 Independent and Dependent Events
Check It Out! Example 1
a. A number cube lands showing an odd number. It is rolled a second time and lands showing a 6.
Tell whether each set of events is independent or dependent. Explain you answer.
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.
Holt Algebra 1
10-7 Independent and Dependent Events
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.
Holt Algebra 1
10-7 Independent and Dependent Events
To determine the probability of two independent events, multiply the probabilities of the two events.
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.
Holt Algebra 1
10-7 Independent and Dependent Events
Holt Algebra 1
10-7 Independent and Dependent Events
Example 2A: 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?
Because the first marble is replaced after it is selected, the sample space for each selection is the same. The events are independent.
Holt Algebra 1
10-7 Independent and Dependent Events
Example 2A Continued
P(red, green) = P(red) P(green)
The probability of selecting red
is , and the probability of
selecting green is .
Holt Algebra 1
10-7 Independent and Dependent Events
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.
Holt Algebra 1
10-7 Independent and Dependent Events
Check It Out! Example 2
An experiment consists of spinning the spinner twice. What is the probability of spinning two odd numbers?
The result of one spin does not affect any following spins. The events are independent.
With 6 numbers on the spinner, 3 of which are odd, the probability of landing on two odd numbers is
P(odd, odd) = P(odd) P(odd)• .
Holt Algebra 1
10-7 Independent and Dependent Events
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.
Probability of drawing a red marble on the first draw
Holt Algebra 1
10-7 Independent and Dependent Events
Probability of drawing a red marble on the seconddraw
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.
Holt Algebra 1
10-7 Independent and Dependent Events
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.
Holt Algebra 1
10-7 Independent and Dependent Events
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?
Holt Algebra 1
10-7 Independent and Dependent Events
Example 3 Continued
11 Understand the Problem
The answer will be the probability that a bag of chips will be chosen after a bag of pretzels is chosen.
List the important information:
• Grant chooses a bag of pretzels from 6 bags of pretzels and 10 bags of chips.
• Iris chooses a bag of chips from 5 bags of pretzels and 10 bags of chips.
Holt Algebra 1
10-7 Independent and Dependent Events
22 Make a Plan
After Grant selects a bag, the sample space changes. So the events are dependent.
Example 3 Continued
After Grant selects a bag, the sample space changes. So the events are dependent.
Draw a diagram.
Grant chooses from: Iris chooses from:
pretzels
chips
Holt Algebra 1
10-7 Independent and Dependent Events
Solve33
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.
Example 3 Continued
The probability that Grant selects a bag of pretzels and Iris selects a bag of chips is .
Holt Algebra 1
10-7 Independent and Dependent Events
Example 3 Continued
Drawing a diagram helps you see how the sample space changes. This means the events are dependent, so you can use the formula for probability of dependent events.
44 Look Back
Holt Algebra 1
10-7 Independent and Dependent Events
Check It Out! Example 3
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?
Holt Algebra 1
10-7 Independent and Dependent Events
Check It Out! Example 3 Continued
11 Understand the Problem
The answer will be the probability that a red marble will be chosen after a blue marble is chosen.
List the important information:
• A blue marble is chosen from a bag containing 10 red, 12 white, and 8 blue marbles.
• Then a red marble is chosen from a bag of 10 red, 12 white, and 7 blue marbles.
Holt Algebra 1
10-7 Independent and Dependent Events
22 Make a Plan
After the first selection, the sample space changes. So the events are dependent.
Draw a diagram.
Check It Out! Example 3 Continued
Second choice from:First choice from:
Holt Algebra 1
10-7 Independent and Dependent Events
Solve33
P(blue and red) = P(blue) P(red after blue)•
Check It Out! Example 3 Continued
One of 8 blue marbles is selected from a total of 30 marbles. Then one of 10 red marbles is selected from the 29 remaining marbles.
The probability that first a blue marble is selected and then a red marble is selected is .
Holt Algebra 1
10-7 Independent and Dependent Events
Look Back44
Drawing a diagram helps you see how the sample space changes. This means the events are dependent, so you can use the formula for probability of dependent events.
Check It Out! Example 3 Continued
Holt Algebra 1
10-7 Independent and Dependent Events
Tell whether each set of events is independent or dependent. Explain your answer.
Lesson Quiz: Part I
1. flipping two different coins and each coin landing showing heads
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
Independent; the flip of the first coin does not affect the sample space for the flip of the second coin.
Dependent; there are fewer cards to choose from when drawing the black card.
Holt Algebra 1
10-7 Independent and Dependent Events
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?
Holt Algebra 1
10-7 Independent and Dependent Events
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?
