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You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent...

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You can do this! 7 th Probability
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Page 1: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

You can do this!

7th Probability

Page 2: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

EventOutcomeProbabilitySample SpaceCompound EventsIndependent EventDependent EventTree Diagram Organized ListCounting PrincipleExperimental ProbabilityTheoretical Probability

Important Probability Terms

Page 3: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

P = 1P = 0.5P = 0.25P = 0

It’ll definitely happen!!!

It’ll NEVER happen!!!

It might happen

P = 0.75

There is a strong

chance it’ll happen

It is not very likely it’ll happen.

Impossible Event Certain Event

Likelihood

Page 4: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

P = 1P = 0.5P = 0.25P = 0

It’ll definitely happen!!!

It’ll NEVER happen!!!

It might happen

P = 0.75

There is a strong

chance it’ll happen

It is not very likely it’ll happen.

Possible Events:

1. The likelihood of having homework tonight.2. The likelihood of having a tornado warning

today.3. The likelihood of having a two hour delay

tomorrow.

Can you think of one?

Page 5: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Real World Probability

Page 6: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

A spinner has 4 equal sections colored

blue, yellow, green, and red. What are the chances of landing on blue after spinning the spinner?Experiment: spinning the

spinner.Outcome: possibilities (yellow,

blue, green or red).Event: Landing on blue.Probability: Favorable event /

possible outcomes.

Applying Vocabulary

Page 7: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

ProbabilityWhat is probability?

The likelihood of an event occurring.

Probability = _______________________

What are the odds of flipping a coin and landing on heads?

Page 8: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Theoretical ProbabilityWhen all possible events or outcomes are equally likely to occur, the theoretical probability can be found without collecting data from an experiment.

When you flip a coin there are two possible outcomes

P (event) =Number of favorable outcomes

Total number of possible outcomes

Page 9: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Experimental ProbabilityData is collected through observations or experiments.

Each result from the experiment is called an event.

The probability of an event is equal to the number of times an event occurs divided by the total number of experiments.

P (event) =Number of times an event occurs

Total number of experiments

Page 10: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

P (event) =Number of times an event occurs

Total number of experiments

Experimental Probability

Event = scoring a basket

Number of baskets scoredNumber of shots taken

102131

Page 11: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

The probability of rolling a 2 on a 6 sided number cube.

After rolling a die 50 times, the number of times you rolled a 2.

The probability of drawing an ace based off of choosing 15 cards from a deck at random.

The probability of choosing an ace from a deck of cards.

Experimental or Theoretical?

Theoretical

Theoretical

Experimental

Experimental

Page 12: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

A bag contains 3 white marbles, 5 blue marbles and 7 red marbles. What is the probability of drawing a blue marble at random?

How many marbles are blue?How many marbles all together?What is the probability as a fraction, decimal

and percent?

Let’s Start Using It!

Page 13: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

If you shuffle a deck of cards and draw a card at random, what is the probability that the card you chose would be a king?

Questions to ask yourself…How many cards are in a deck?How many kings are in a deck?What is the probability?

Another Example

Page 14: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

If you rolled a six sided die, what is the probability that you would roll and even number?

A. 1/6 C. 6/6

B. 2/6 D. 1/2

Your Turn

Page 15: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

A bag contains 6 black marbles, 9 red marbles, 12 white marbles, and 3 green marbles. What is the probability of drawing a red marble?

A. 3/10 C. 3/5

B. 6/30 D. 12/30

Try Another

Page 16: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

**OR = ADD**If rolling a 6 sided die, what is the probability

of rolling a 2 or a 6?

In this case you could have a successful outcome if you roll a 2 or a 6.

Number of favorable outcomes Number of total outcomes

Mutually Exclusive Events

=

Page 17: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

If you were to spin this spinner, what would the probability be of landing on bankrupt or lose turn?

P (bankrupt or lose turn)

An Example

Page 18: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

A bag contains 2 black marbles, 9 red marbles, 12 white marbles, and 5 green marbles. What is the probability of drawing a black or a green marble?

Another Example

Page 19: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

What is the probability of picking a card out of a standard deck and drawing a jack or 4?

A. C.

B. D.

Your Turn

Page 20: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

What is the probability of picking a card out of a standard deck and drawing a queen, king, or jack?

A. C.

B. D.

Try Again

Page 21: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Probability Worksheet

PLEASE SHOW YOUR WORK!!

No homework passes for this assignment!(Sorry)

Homework

Page 22: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

What is the probability of drawing a jack out of a standard deck of cards?

What is the probability of rolling a 4 or 5 on a six sided number cube?

*If I draw cards from a deck 50 times to determine the probability of pulling a face card, am I using theoretical or experimental probability?

What is the probability of drawing a red ace from a standard deck of cards?

Page 23: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Tree Diagrams

Shows all possible outcomes in an

organized drawing.

Page 24: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue?

First write a list down the paper of the first item, in this case 1 to 5

12345

Page 25: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue?

Now determine how many options there are for the second item

There are 3 options:Red

White

Blue

Page 26: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue?

Draw “branches” off of each number. One for each second item, in this case 3.

12345

Page 27: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue?

At the end of each branch, write one of the three options from the 2nd items given.

1

2

3

4

5

RWB

RWB

RWB

RWB

RWB

What is the chance of choosing the color red?

Page 28: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

PROBLEM: What is the chance of choosing the color red?

There are five different times the color red could be chosen from all 15 options

The chance of having the color red is 5/15 or reduced is 1/3

Page 29: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

How many combinations of sandwiches can you make with the following options?

Types of Bread Fillings*Wheat *Cheese*Italian *Ham*Rye *Turkey

*Salami

Let’s Try

Page 30: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Your turn! Give the total number of outcomes

of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram.

Page 31: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Another way to determine how many possibilities. Create a list of all options.

How many possible outcomes are there with a red, blue or green sock and a black or white shirt?

List: Red & Black, Red & White, Blue & Black, Blue & White, Green & Black, Green & White.

How many outcomes?

Organized Lists

Page 32: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Shirts Pants*Blue *Black*Red *Brown*Green*Yellow

Let’s Create Our Own

Page 33: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

YES!

Multiply the number of possibilities in the first set by the number of possibilities in the second set.

Example:2 colors (red, blue), numbers 1 -5 numbers: 2 × 5 =

10

List: red 1, red 2, red 3, red 4, red 5, blue 1, blue 2, blue 3, blue 4, blue 5

Is there a shortcut?

Page 34: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

How many combinations can you have with 3 colors and 10 numbers?

A. 13 C. 30

B. 15 D. 7

Try the Shortcut

Page 35: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

How many combinations are in a sample space with rolling 2 dice and tossing a coin?

A. 72 C. 12

B. 80 D. 36

Try the Shortcut

Page 36: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

What is it?An event that consists of two or more simple

events.

Steps:*Determine all outcomes for each event.*Multiply number of outcomes.*Find all favorable events.

Compound Events

Page 37: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.Landing on heads after tossing a coin AND

rolling a 5 on a single 6-sided die. Choosing a marble from a jar AND landing on

heads after tossing a coin. Choosing a 3 from a deck of cards, replacing it,

AND then choosing an ace as the second card. Rolling a 4 on a single 6-sided die, AND then

rolling a 1 on a second roll of the die.

Independent Events

Page 38: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Multiplication Rule :   When two events, A and B, are independent, the probability of both occurring is:   P(A and B) = P(A) · P(B)

Independent Events

Page 39: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Each spinner is divided into equal sections. The two spinners are spun together . What is the probability of landing on blue and an even number?

Independent Event

Page 40: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.

Another Example

Page 41: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. What is the probability of choosing a green and then a yellow marble?

A. C.

B. D.

Your Turn

Page 42: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

What is the probability of rolling an even number on a die and tossing a coin and landing on tails?

A. 1/2 C. 1/4

B. 1/8 D. 2/3

Try again

Page 43: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Multiplication Rule 2:   When two events, A and B, are dependent, the probability of both occurring is:   P(A and B)  =  P(A) · P(B|A)

Experiment 1:   A card is chosen at random from a standard deck of 52 playing cards. Without replacing it, a second card is chosen. What is the probability that the first card chosen is a queen and the second card chosen is a jack?

Dependent Events

Page 44: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Mr. R needs two students to help him with a science demonstration for his class of 18 girls and 12 boys. He randomly chooses one student who comes to the front of the room. He then chooses a second student from those still seated. What is the probability that both students chosen are girls?

Another Example

Page 45: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

Three cards are chosen at random from a deck of 52 cards without replacement. What is the probability of choosing 3 aces?

A. C.

B. D.

Your Turn

Page 46: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

In Mr. M’s room, students are being assigned to group projects by drawing colored chips from a bag. Once selected, the marbles will not be returned to the bag. There are 4 blue chips, 5 green chips, 5 red, 4 yellow chips, 4 black chips and 4 white chips. What is the probability the first and second students will draw yellow chips?

A. 1/3 C. 2/650

B. 6/325 D. 2/3

Another Try

Page 47: You can do this!. Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle.

What is the probability of rolling a 2 or 3 on a six sided number cube?

What is the probability of drawing a six of clubs from a standards deck of playing cards?

*What is the probability of flipping a coin and landing on heads and rolling a die and landing on 2 or 4?

Two cards are drawn from a standard deck of playing cards without replacing it. What is the probability that the first card is an ace and the second is a 4?


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