7 Independent and Dependent Events

How does using the Fundamental Counting Principle, tree diagrams and sample space help you find the probability of certain events?

Do Now

Let's Review: Compound EventConsists of two or more simple events

P(Event A) P(Event B)*Use the Counting Principle to find the number of total outcomes.

*The Probability of a  Compound Event is the fraction of outcomes in the same space for which the compound event occurs.

P(R,H) =

P(Y,T) =

7 Independent and Dependent Events

Let's Review: Compound EventConsists of two or more simple events

P(Event A) P(Event B)*Use the Counting Principle to find the number of total outcomes.

*The Probability of a  Compound Event is the fraction of outcomes in the same space for which the compound event occurs.

P(R,H) =

P(Y,T) =

1/8

1/8

Independent Events

Two or more events in which the outcome of one event does not affect the outcome of the other event(s)

Examples

1. Spinning a spinner and flipping a coin

2. Spinning two different spinners

3. Drawing a marble and flipping a coin

7 Independent and Dependent Events

Two spinners are spun. What is the probability that both spinners will show an odd number?

P(first spinner lands on odd, second spinner lands on odd) =

Let's Practice: Independent Events

Two spinners are spun. What is the probability that both spinners will show an odd number?

P(first spinner lands on odd, second spinner lands on odd) =

Let's Practice: Independent Events

7 Independent and Dependent Events

P(landing on tails and rolling a 3) =

P(landing on head and a prime number) =

Answer on next slide

P(landing on tails and rolling a 3) =

P(landing on head and a prime number) =

Answer on next slide

7 Independent and Dependent Events

Dependent EventsTwo or more events in which the outcome of one event DOES affect the outcome of the other.

Examples1. Drawing a marble from a jar, and 

    then drawing another marble

2. Picking two cards at random without 

    replacement 

The bag contains 13 marbles - 4 red, 3 green, 3 blue, and 3 purple .You are picking 2 marbles at random, and you are not replacing the marble you picked.P(first marble is purple, second marble is purple) =

P(a red marble, then a green marble) =

Let's Practice: Dependent Events

7 Independent and Dependent Events

The bag contains 13 marbles - 4 red, 3 green, 3 blue, and 3 purple .You are picking 2 marbles at random, and you are not replacing the marble you picked.P(first marble is purple, second marble is purple) =

P(a red marble, then a green marble) =

Let's Practice: Dependent Events

The bag contains 13 marbles - 4 red, 3 green, 3 blue, and 3 purple .You are picking 2 marbles at random, and you are not replacing the marble you picked.P(first marble is purple, second marble is purple) =

P(a red marble, then a green marble) =

Let's Practice: Dependent Events

7 Independent and Dependent Events

A Standard Deck of CardsTotal ­ 52

 26 Red 26 Black

13 Hearts 13 Clubs13 Diamonds 13 Spades

Four of a KindNumbers 2 ­10

Face Cards ­ Jack, Queen and KingAces

You are picking 2 cards at random from a standard deck of cards without replacement.

P(first card is a Jack, second card is a Jack) =

P(first card is a diamond, second card is a spade) =

7 Independent and Dependent Events

You are picking 2 cards at random from a standard deck of cards without replacement.

P(first card is a Jack, second card is a Jack) =

P(first card is a diamond, second card is a spade) =

Amina takes a coin from the jar and does not 

replace it. Then you take a coin form the jar.

7

Rashod guesses on two multiple choice questions.

6

A woman chooses a lily from one bunch of flowers and then chooses a tulip from a different bunch. 

5

Briana chooses a marble from a bag and replaces it, then Clarence chooses a marble from the bag.

4

Briana chooses a marble from a bag and keeps it, then Clarence chooses a marble from the bag. 

3

Chelsea flips a coin twice.2

Sort into categories.

Independent DependentRayquan rolls a cube 

numbered 1 ­ 6 and flips a coin.

1

7 Independent and Dependent Events

Amina takes a coin from the jar and does not 

replace it. Then you take a coin form the jar.

7

Rashod guesses on two multiple choice questions.

6

A woman chooses a lily from one bunch of flowers and then chooses a tulip from a different bunch. 

5

Briana chooses a marble from a bag and replaces it, then Clarence chooses a marble from the bag.

4

Briana chooses a marble from a bag and keeps it, then Clarence chooses a marble from the bag. 

3

Chelsea flips a coin twice.2

Sort into categories.

Independent Dependent

pageNotes

Rayquan rolls a cube numbered 1 ­ 6 and flips 

a coin.

1

Exit Ticket: On the back of your packet, create two probability word problems for your table to solve. One word problem should involve independent events and the other should involve dependent events ­ there should be two questions for each scenario.