ProbabilityProbability

Tree Diagram: Tree Diagram: A diagram with A diagram with branches branches that is used to list all possible outcomes.that is used to list all possible outcomes.

Example: Example: Meal choices:Meal choices: Burger, hot dog, Pizza Burger, hot dog, Pizza Drinks:Drinks: coke or sprite coke or sprite

Sample space: Sample space: A list of A list of all the possible all the possible outcomes.outcomes. Example: The sample space for rolling a dice isExample: The sample space for rolling a dice is

{1, 2, 3, 4, 5, 6}.{1, 2, 3, 4, 5, 6}.

Counting Principle: Counting Principle: a way to find the a way to find the number of possible outcomes of an event.number of possible outcomes of an event. **Just multiply the number of ways **Just multiply the number of ways each activity each activity

can occur.can occur.

Try the followingTry the following Andy flips a coin and spins a spinner with 3 equal

sections marked A, B, C. a) Draw a tree diagram, b) What is the sample space (i.e. all possible outcomes)? How many outcomes are in the sample space?

HA TA

HB TB 6 outcomes

HC TC

For the lunch special at Nick’s Deli, customers can create their own sandwich by selecting 1 type of bread and 1 type of meat from the selection below.

ca) In the space below, list all the possible sandwich combinations using 1 type of bread and 1 type of meat.

WC RC

WRb RRb

b) If Nick decides to add whole wheat bread as another option, how many possible sandwich combinations will there be?

6 outcomes

Helen is preparing candy bags for the children at a party. She has 2 flavors of lollipops, 4 types of candy bars, and 6 flavors of chewy candies. If each bag contains one piece of each type of candy, what is the total number of possible candy combinations for the bags?

A) 12 B) 15 C) 36 D) 48

Peter has 6 sweatshirts, 4 pairs of jeans, and 3 pairs of shoes. How many different outfits can Peter make using one sweatshirt, one pair of jeans, and one pair of shoes?

A) 13 B) 36 C) 72 D) 144

Erin wants to make a sandwich from the main ingredients shown in the table below.

In the space below, list all the possible ways Erin can make a sandwich using one type of bread and one main ingredient.

SP SH ST SEWP WH WT WERP RH RT RE

ProbabilityProbability: is the : is the likelihood that an likelihood that an event will occur.event will occur. Probability of getting a tail when tossing a coinProbability of getting a tail when tossing a coin

Experiment: Experiment: aan activity involving chance, such as rolling a cube Tossing a coin is theTossing a coin is the experiment experiment

Trial: Trial: Each repetition or observation of an experiment Each time you toss the coin is a Each time you toss the coin is a trialtrial

Outcome: Outcome: A possible result of an event.A possible result of an event. Example: Heads or tails are possible Example: Heads or tails are possible outcomesoutcomes

when tossing a coinwhen tossing a coin

Event:Event: A set of one or more outcomes Example: Getting a heads when you toss

the coin is the event Compliment of an Event: Compliment of an Event: The outcomes The outcomes

that are not the eventthat are not the event Example: Probability of rolling a 4 = 1/6. Not Example: Probability of rolling a 4 = 1/6. Not

rolling a 4 = 5/6.rolling a 4 = 5/6.

Probability is always between 0 and 1Probability is always between 0 and 1..

Probability = 0 means that the event will Probability = 0 means that the event will NEVER happen. NEVER happen. Example: The probability that the Bills will win the Example: The probability that the Bills will win the

Super Bowl this year.Super Bowl this year.

Probability = 1 means the event will Probability = 1 means the event will ALWAYS happen.ALWAYS happen. Example: The probability that Christmas will be on Example: The probability that Christmas will be on

December 25December 25thth next year. next year.

______________________________

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Rolling a 0 on a number cube Rolling a 0 on a number cube ImpossibleImpossible

Rolling a number less than 3 on a number Rolling a number less than 3 on a number cubecube Unlikely Unlikely

Rolling an even number on a number cube Rolling an even number on a number cube Equally likelyEqually likely

Rolling a number greater than 2 on a diceRolling a number greater than 2 on a dice LikelyLikely

Rolling a number less than 7 on a number Rolling a number less than 7 on a number cubecube CertainCertain

Experimental Probability: Experimental Probability: is based on is based on an an experiment. The probability of what experiment. The probability of what ACTUALLY did happened.ACTUALLY did happened.

Try the followingTry the following Example 1: During football practice, Sam made

12 out of 15 field goals. What is the probability he will make the field goal on the next attempt?3

12/15

Example 2: Ms. Sekuterski’s student have taken out 85 books from the library. 35 of them were fiction. What is the probability that the next book checked out will be a fiction book?

35/38

Example 3: Emma made 9 out of 15 foul shots during the first 3 quarters of her basketball game. What is the probability that the next time she takes a foul shot she will make it?

9/15

Example 4: Christina scored an A on 7 out of 10 tests. What is the probability she will score an A on her next test?

7/10

Theoretical ProbabilityTheoretical Probability: the probability : the probability of of what should happenwhat should happen.. It’s based on a rule:It’s based on a rule:

# of favorable outcomes# of favorable outcomes

# of possible outcomes# of possible outcomes Example: Rolling a dice andExample: Rolling a dice and getting a 3 =getting a 3 =

6

1

Example 1: Andy has 10 marbles in a bag. 6 are white and 4 are blue. Find the probability as a fraction, decimal, and percent of each of the following:a) P(blue marble)

4/10b) P(white marble)

6/10

Example 2: If there are 12 boys and 13 girls in a class, what is the probability that a girl will be picked to write on the board?

13/25

Example 3: There are 8 black chips in a bag of 30 chips. What is the probability of picking a black chip from the bag?

8/30

Example 4: There are 2 small, 5 medium, and 3 large dogs in a yard. What is the probability that the first dog to come in the door is small?

2/10

Example 5: What is the probability of getting a tail when flipping a coin?

1/2

Example 6: What is the probability of rolling a 4 on a die?

1/6

IndependentIndependent: : the outcome of one the outcome of one event DOESN’T effect the probability event DOESN’T effect the probability of another eventof another event

Example: Find the probability of choosing a Example: Find the probability of choosing a green marble at random from a bag green marble at random from a bag containing 5 green and 10 white marbles containing 5 green and 10 white marbles and then flipping a coin and getting tails.and then flipping a coin and getting tails.

5/15 x ½ = 5/30 = 1/65/15 x ½ = 5/30 = 1/6

ReplacementReplacement: : DOESN’T effect the DOESN’T effect the probability of another eventprobability of another event

Example: Example: A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips.  One paperclip is taken from the drawer and then replaced.  Another paperclip is taken from the drawer.  What is the probability that the first paperclip is red and the second paperclip is blue?

3/12 x 5/12 = 15/144 = 5/483/12 x 5/12 = 15/144 = 5/48

DependentDependent: : the outcome of one event the outcome of one event DOES effect the probability of another DOES effect the probability of another eventevent

Example: Example: Micah has five $1 bills, three $10 bills, and two $20 bills in her wallet. She picks two bills at random. What is the probability of her picking the two $20 bills?

2/10 x 1/9 = 2/90 = 1/452/10 x 1/9 = 2/90 = 1/45

Without ReplacementWithout Replacement: : DOES effect DOES effect the probability of another eventthe probability of another event

Example: Example: A bag contains 3 blue and 5 red marbles. Find the probability of drawing 2 blue marbles in a row without replacing the first marble.

3/8 x 2/7 = 6/56 = 3/283/8 x 2/7 = 6/56 = 3/28

OR ProbabilitiesOR Probabilities: : Add the Add the probabilitiesprobabilities

Example: Example: Rolling either a 5 or a 6 on a 1 – 6 number cube.

P(5 or 6) 

1/6 + 1/6 = 2/6 = 1/31/6 + 1/6 = 2/6 = 1/3

 Example 2: Choosing either an A or an E from the letters in the word mathematics.

 

P(A or E)

2/11 + 1/11 = 3/112/11 + 1/11 = 3/11

1. Spinning red or green on a spinner that has 4 sections (1 red, 1green, 1 blue, 1 yellow) 

¼ + ¼ = 2/4 = ½  

2. Drawing a black marble or a red marble from a bag that contains 4 white, 3 black, and 2 red marbles.  3/9 + 2/9 = 5/9

 3. Choosing either a number less than 3 or a number greater than 12 from a set of cards numbered 1 – 20.

2/20 + 8/20 = 10/20 = ½

  

AND ProbabilitiesAND Probabilities: : Multiply the Multiply the probabilitiesprobabilities

Example 1: A die is rolled.  What is the probability that the number rolled is greater than 2 and even?

 

P( >2 and Even) 

Example 2: From a standard deck of cards, one card is drawn.  What is the probability that the card is black and a jack?