Simple Probability and Odds

Objectives:·Find the probability of a simple event

·Find the odds of a simple event.

DefinitionsProbability·The likelihood of an event occurring. The ratio of the number of favorable outcomes of an event to the total number of possible outcomes.

Example: The probability of rolling a "2" on a die is .61

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

Importance of Probability

Introduction__What_are_the_Chances_.asf

Determining_Probability.asf

A spinner has four equal sections colored yellow, blue, green and red. What are the chances of landing on red with a single spin?

Probability (P) = The number of opportunities for an outcome to occurThe number of possible outcomes

The theoretical probability of the spinner landing on red = .

Formula for probability:

P (red) =

Theoretical Probability

14

14

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?

Probability (P) = The number of opportunities for an outcome to occurThe number of possible outcomes

Formula for probability:

P (not red) =

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 1Total number of sides

=

P (1) =

Theoretical Probability

P (6) =

P (5) =

P (4) =

P (3) =

P (2) =

16

e.g.,

P (Even) = =

A single six-sided die is rolled. What is the probability of rolling an even number?

Number of sides with even numbersTotal number of sides

Theoretical Probability

P (Odd) =

A single six-sided die is rolled. What is the probability of rolling an odd number?

P (1, 4, 5, 6) = Number of sides that are not 2 or 3Total number of sides

=

P (1, 2, 3) =

A single six-sided die is rolled. What is the probability of not rolling a 2 or 3?

Theoretical Probability

A single six-sided die is rolled. What is the probability of not rolling a 4, 5 or 6?

P (red) = Number of red marblesTotal 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?

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?

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?

P (not red) = Number of marbles that are not red

Total number of marbles=

What is the probability you will choose a red or yellow marble?

P (red or yellow) =

Theoretical Probability

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.

Was the car race fair? Why or why not?

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 purple marble from a jar containing three purple, two green and eight orange marbles?

What is the probability of choosing a queen or a 10 from a standard deck of cards?

If the letters in "probability" were placed in a hat, what would be the probability of choosing a "b" in a single draw?

Experimental ProbabilityOne 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"

Experimental Probability

Now that you have completed the test, complete the formula:

P (5) = Number of times "5" was rolledTotal 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.

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.

2 dice are rolled and the sum is recorded.

1) What are all the possible outcomes?

1st die

2nd die

1 2 3 4 5 6

1234 56

Sum of rolling 2 dice

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

Odds

1) Find the odds of rolling a number greater than 4

Begin with the sample space {1, 2, 3, 4, 5, 6}

Successes : Failures

:

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 nameThe United States of America.

a) the letter a b) a vowel

c) a lowercase letter

3) If the probability that an event will occur is , what are the odds that it will occur?37

Classwork:

Complete the Study Guide and Intervention p. 29-30

odds on front and back (due at end of class)

Attachments

Determining_Probability.asf

Introduction__What_are_the_Chances_.asf