Holt CA Course 1 8-6 Independent and Dependent Events Warm Up Warm Up California Standards...

Holt CA Course 1

8-6 Independent and Dependent Events

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California StandardsCalifornia Standards

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Holt CA Course 1


Warm UpWrite each answer as a ratio, as a decimal, and as a percent.

A 1–6 number cube is rolled.

1. What is the probability that an even number will result?

2. What is the probability that the number will be prime?

12

12

, 0.5, 50%

, 0.5, 50%

Holt CA Course 1


SDAP3.5 Understand the difference between independent and dependent events.Also covered: SDAP3.3, SDAP3.4

California Standards

Holt CA Course 1


Objective:Objective: You will learn You will learn how to (YWLHT) identify how to (YWLHT) identify independent and independent and dependent events and dependent events and find the probability of find the probability of independent events.independent events.

Holt CA Course 1


Vocabulary

independent eventsdependent events

Holt CA Course 1


Raji and Kara must each choose a topic from a list of topics to research for their class. If Raji can choose the same topic as Kara and vice versa, the events are independent. For independent events, the occurrence of one event has no effect on the probability that a second event will occur.

If once Raji chooses a topic, Kara must choose from the remaining topics, then the events are dependent. For dependent events, the occurrence of one event does have an effect on the probability that a second event will occur.

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Decide whether the set of events are dependent or independent. Explain your answer.

Example 1: Determining Whether Events Are Independent or Dependent

A. Kathi draws a 4 from a set of cards numbered 1–10 and rolls a 2 on a number cube.

Since the outcome of drawing the card does not affect the outcome of rolling the cube, the events are independent.

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B. Yuki chooses a book from the shelf to read, and then Janette chooses a book from the books that remain.

Since Janette cannot pick the same book that Yuki picked, and since there are fewer books for Janette to choose from after Yuki chooses, the events are dependent.

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C. Imad chooses a pencil from a drawer, puts it back, and then chooses a second pencil. Both pencils are red. The drawer holds the same pencils each time.

Since Imad replaces the first pencil, the outcome of picking the first pencil does not affect the outcome of picking the second pencil. The events are independent.

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Check It Out! Example 4

A. Joann flips a coin and gets a head. Then she rolls a 6 on a number cube.

Since flipping the coin does not affect the outcome of rolling the number cube, the events are independent.


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B. Annabelle chooses a blue marble from a set of three, each of different colors, andthen Louise chooses a second marble from the remaining two marbles.

Since they are picking from the same set of three marbles, they cannot pick the same color marble. The events are dependent.


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C. Lisa chooses a pen from a bag, puts it back, and then chooses a second pen. Both pens are blue. The bag holds the same pens each time.

Since Lisa replaces the first pen, the outcome of picking the first pen does not affect the outcome of picking the second pen. The events are independent.

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To find the probability that two independent events will happen, multiply the probabilities of the two events.

Probability of Two Independent EventsProbability of Two Independent Events

== ••

Probability of both events

Probability offirst event

Probability of second event

PP((AA and and BB)) PP((AA)) PP((BB))

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Find the probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails.

Example 7: Finding the Probability of Independent Events

Holt CA Course 1


Find the probability of choosing a green marble at random from a bag of 5 green and 10 white marbles and then flipping a coin and getting tails.

Example 7: Finding the Probability of Independent Events

The outcome of choosing the marble does not affect the outcome of flipping the coin, so the events are independent.

P(green and tails) = P(green) · P(tails) 1 3= · 1

2

The probability of choosing a green marble and acoin landing on tails is .1

6

Holt CA Course 1

8-6 Independent and Dependent EventsCheck It Out! Example 8

Find the probability of choosing a red marble at random from a bag containing 5 red and 5 white marbles and then flipping a coin and getting heads.

Holt CA Course 1

8-6 Independent and Dependent EventsCheck It Out! Example 8

Find the probability of choosing a red marble at random from a bag containing 5 red and 5 white marbles and then flipping a coin and getting heads.

The outcome of choosing the marble does not affectthe outcome of flipping the coin, so the events are independent.

P(red and heads) = P(red) · P(heads) 1 2= · 1

2

The probability of choosing a red marble and acoin landing on heads is .1

4

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A basketball player has a 60% chance of making a free throw on each attempt. If the chance of making one free throw is independent of the chance of making the next free throw, what is the probability that the player will make 2 free throws in a row?

Example 9: Sports Application

P(making 1st free throw and 2nd free throw) = P(1st free throw) ∙ P(2nd free throw)

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Example 9 Continued

= 60% ∙ 60%

= 0.60 ∙ 0.60

= 0.36

The probability of the basketball player making 2 free throws in a row is 36%.

Substitute 60% for P(1st free throw) and 60% for P(2nd free throw).

Write the percents as decimals.

Multiply.

= 36% Write the decimal as a percent.

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A professional bowler has a 40% chance of bowling a strike on each attempt. If the chance of bowling a strike is independent of the chance of bowling a strike in the next frame, what is the probability that the player will bowl 2 strikes in a row?


P(1st strike and 2nd strike) = P(1st strike) ∙ P(2nd strike)

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Check It Out! Example 10 Continued

= 40% ∙ 40%

= 0.40 ∙ 0.40

= 0.16

The probability of the professional bowler bowling 2 strikes in a row is 16%.

Substitute 40% for P(1st strike) and 40% for P(2nd strike).

Write the percents as decimals.

Multiply.

= 16% Write the decimal as a percent.

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Home Home

LearningLearning

Fishing!

On-Line On-Line TutoringTutoring

Games!

Take a Chance!

Pondability

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Lesson QuizDecide whether each event is independent or dependent. Explain.

1. Mary chooses a game piece from a board game, and then Jason chooses a game piece from three remaining pieces.

2. Find the probability of spinning an evenly dividedspinner numbered 1–8 and getting a composite number on one spin and getting an odd number on a second spin.

Dependent; Jason has fewer pieces from which to choose.

316

3. A baseball player has a 10% chance of hitting the ball on each turn at bat. What is the probability that the player will hit the ball on each of his next 2 turns at bat?

1%

Holt CA Course 1 8-6 Independent and Dependent Events Warm Up Warm Up California Standards...

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