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7th Probability You can do this!

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**Important Probability Terms**

Event Outcome Probability Sample Space Compound Events Independent Event Dependent Event Tree Diagram Organized List Counting Principle Experimental Probability Theoretical Probability

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**Likelihood Impossible Event Certain Event P = 1 P = 0 P = 0.25 P = 0.5**

It is not very likely it’ll happen. It might happen There is a strong chance it’ll happen It’ll definitely happen!!! It’ll NEVER happen!!!

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**The likelihood of having homework tonight. **

Possible Events: The likelihood of having homework tonight. The likelihood of having a tornado warning today. The likelihood of having a two hour delay tomorrow. Can you think of one? P = 1 P = 0 P = 0.25 P = 0.5 P = 0.75 It is not very likely it’ll happen. It might happen There is a strong chance it’ll happen It’ll definitely happen!!! It’ll NEVER happen!!!

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**Real World Probability**

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**Applying Vocabulary 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.

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**Probability What is probability? The likelihood of an event occurring.**

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

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**Theoretical Probability When you flip a coin there are**

When 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

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**Experimental Probability**

Data 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

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**Experimental Probability**

P (event) = Number of times an event occurs Total number of experiments Event = scoring a basket 2 1 1 3 1 Number of baskets scored Number of shots taken

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**Experimental or Theoretical?**

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. Theoretical Experimental Experimental Theoretical

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Let’s Start Using It! 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?

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Another Example 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?

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Your Turn 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

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Try Another 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

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**Mutually Exclusive Events**

**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 =

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**An Example If you were to spin this spinner, what**

would the probability be of landing on bankrupt or lose turn? P (bankrupt or lose turn)

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Another Example 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?

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Your Turn What is the probability of picking a card out of a standard deck and drawing a jack or 4? A. C. B. D.

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Try Again What is the probability of picking a card out of a standard deck and drawing a queen, king, or jack? A. C. B. D.

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Homework Probability Worksheet PLEASE SHOW YOUR WORK!! No homework passes for this assignment! (Sorry)

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**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?

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Tree Diagrams Shows all possible outcomes in an organized drawing.

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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 1 2 3 4 5

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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

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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. 1 2 3 4 5

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**What is the chance of choosing the color red?**

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 R W B What is the chance of choosing the color red? R W B R W B R W B R W B

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**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

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Let’s Try How many combinations of sandwiches can you make with the following options? Types of Bread Fillings *Wheat *Cheese *Italian *Ham *Rye *Turkey *Salami

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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.

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Organized Lists 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?

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Let’s Create Our Own Shirts Pants *Blue *Black *Red *Brown *Green *Yellow

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Is there a shortcut? 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

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Try the Shortcut How many combinations can you have with 3 colors and 10 numbers? A C. 30 B D. 7

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Try the Shortcut How many combinations are in a sample space with rolling 2 dice and tossing a coin? A C. 12 B D. 36

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**Compound Events What is it? Steps:**

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.

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Independent Events 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.

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

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Independent Event 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?

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Another Example 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.

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Your Turn 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.

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Try again 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

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Dependent Events 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?

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Another Example 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?

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Your Turn 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.

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Another Try 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

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**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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