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**Simple Probability and Odds**

Objectives: ·Find the probability of a simple event ·Find the odds of a simple event.

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**Definitions Probability Simple Event Sample Space Equally Likely Odds**

·The likelihood of an event occurring. The ratio of the number of favorable outcomes of an event to the total number of possible outcomes. 6 1 Example: The probability of rolling a "2" on a die is Simple Event ·a single event Example: Rolling a die Sample Space ·the list of all possible outcomes Example: the sample space for rolling a die = {1, 2, 3, 4, 5, 6} Equally Likely ·outcomes for which the probability of each occurring is equal Example: flipping a coin Odds ·the ratio that compares the number of ways an event can occur (successes) to the number of ways the event cannot occur (failures) ·successes : failures

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**Importance of Probability**

Introduction__What_are_the_Chances_.asf Determining_Probability.asf

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**Theoretical Probability**

A spinner has four equal sections colored yellow, blue, green and red. What are the chances of landing on red with a single spin? Formula for probability: The number of opportunities for an outcome to occur Probability (P) = The number of possible outcomes 1 4 P (red) = 1 4 The theoretical probability of the spinner landing on red =

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**Theoretical Probability**

A spinner has four equal sections colored yellow, blue, green and red. What are the chances of not landing on red with a single spin? Formula for probability: The number of opportunities for an outcome to occur Probability (P) = The number of possible outcomes P (not red) =

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**Theoretical Probability**

A single six-sided die is rolled. What is the probability of rolling a 1, 2, 3, 4, 5 or 6? Number of sides with number 1 1 6 = e.g., Total number of sides P (1) = P (4) = P (2) = P (5) = P (3) = P (6) =

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**Theoretical Probability**

A single six-sided die is rolled. What is the probability of rolling an even number? Number of sides with even numbers P (Even) = = Total number of sides A single six-sided die is rolled. What is the probability of rolling an odd number? P (Odd) =

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**Theoretical Probability**

A single six-sided die is rolled. What is the probability of not rolling a 2 or 3? Number of sides that are not 2 or 3 P (1, 4, 5, 6) = = Total number of sides A single six-sided die is rolled. What is the probability of not rolling a 4, 5 or 6? P (1, 2, 3) =

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**Theoretical Probability**

A pail contains eight red marbles, five blue marbles, six green marbles and three yellow marbles. If a single marble is chosen from the pail, what is the probability it will be red? Blue? Green? Yellow? Number of red marbles P (red) = = Total number of marbles P (blue) = P (green) = P(yellow) = What color are you most likely to get if you pick a single marble out of the pail? What color are you least likely to get?

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**Theoretical Probability**

A pail contains eight red marbles, five blue marbles, six green marbles and three yellow marbles. If a single marble is chosen from the pail, what is the probability it will not be red? Number of marbles that are not red P (not red) = = Total number of marbles What is the probability you will choose a red or yellow marble? P (red or yellow) =

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**A Fair Race? For this part of the lesson, you will need a die.**

Roll the die. If the die lands on 1 or 2, the green car will advance one space. If the die lands on 3, 4, 5 or 6, the red car will advance one space. The first car to reach the last square is the winner.

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Was the car race fair? Why or why not?

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**Use your understanding of theoretical probability to answer the following questions:**

What is the probability of choosing a king from a standard deck of cards? What is the probability of choosing a queen or a 10 from a standard deck of cards? What is the probability of choosing a purple marble from a jar containing three purple, two green and eight orange marbles? If the letters in "probability" were placed in a hat, what would be the probability of choosing a "b" in a single draw?

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**Experimental Probability**

One way to estimate the probability of an event is to conduct an experiment. The theoretical probability of rolling "5" on a single die is 1/6; however, this does not guarantee the experimental probability will be the same. Let's try an experiment using a single die. Roll the die 50 times. Each time you roll "5", make a check mark in the following table: Rolled "5"

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**Experimental Probability**

Now that you have completed the test, complete the formula: Number of times "5" was rolled P (5) = = Total rolls of the die Was your result different from the theoretical probability of 1/6? Try rolling the die 100 times. Are you closer to the theoretical probability? Why is the result different? Remember: Theoretical probability is what will happen in an ideal situation. Experimental probability is what happens when you actually perform the event.

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1) A class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. P(red or brown) 2)Find the probability of rolling a number greater than two on die. Let's discuss the probabilities based on rolling two dice.

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**2 dice are rolled and the sum is recorded. **

1) What are all the possible outcomes? Sum of rolling 2 dice 2nd die 1 2 3 4 5 6

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Standard Deck of Cards ·52 cards (2 colors: red, black) ·4 suits (diamonds, hearts, spades, clubs) ·13 cards in each suit ·4 face cards in each suit

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Odds Successes : Failures 1) Find the odds of rolling a number greater than 4 Begin with the sample space {1, 2, 3, 4, 5, 6} : success (#s greater than 4) failure (#'s less than or equal to 4) 2) Find the odds of each outcome of a computer randomly picks a letter in the name The United States of America. a) the letter a b) a vowel c) a lowercase letter 3 7 3) If the probability that an event will occur is , what are the odds that it will occur?

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Classwork: Complete the Study Guide and Intervention p odds on front and back (due at end of class)

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Attachments Determining_Probability.asf Introduction__What_are_the_Chances_.asf

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