Probability

 Tree Diagram: A diagram with branches that is used to list all possible outcomes. Example: Meal choices: Burger, hot dog, Pizza Drinks: coke or sprite

Sample space: A list of all the possible outcomes. Sample space: A list of all the possible outcomes. Example: The sample space for rolling a dice is Example: The sample space for rolling a dice is {1, 2, 3, 4, 5, 6}. {1, 2, 3, 4, 5, 6}. Counting Principle: a way to find the number of possible outcomes of an event. Counting Principle: a way to find the number of possible outcomes of an event. **Just multiply the number of ways each activity can occur. **Just multiply the number of ways each activity can occur.

Try 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? HATA HBTB6 outcomes HCTC

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. c a) In the space below, list all the possible sandwich combinations using 1 type of bread and 1 type of meat. WCRC WRbRRb 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. SPSHSTSE WPWHWTWE RPRHRTRE

Probability: is the likelihood that an event will occur. Probability: is the likelihood that an event will occur. Probability of getting a tail when tossing a coin Probability of getting a tail when tossing a coin Experiment: a Experiment: a n activity involving chance, such as rolling a cube Tossing a coin is the experiment Tossing a coin is the experiment Trial: Trial: Each repetition or observation of an experiment Each time you toss the coin is a trial Each time you toss the coin is a trial

Outcome: A possible result of an event. Outcome: A possible result of an event. Example: Heads or tails are possible outcomes when tossing a coin Example: Heads or tails are possible outcomes when 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: The outcomes that are not the event Compliment of an Event: The outcomes that are not the event Example: Probability of rolling a 4 = 1/6. Not rolling a 4 = 5/6. Example: Probability of rolling a 4 = 1/6. Not rolling a 4 = 5/6.

Probability is always between 0 and 1. Probability is always between 0 and 1. Probability = 0 means that the event will NEVER happen. Probability = 0 means that the event will NEVER happen. Example: The probability that the Bills will win the Super Bowl this year. Example: The probability that the Bills will win the Super Bowl this year. Probability = 1 means the event will ALWAYS happen. Probability = 1 means the event will ALWAYS happen. Example: The probability that Christmas will be on December 25 th next year. Example: The probability that Christmas will be on December 25 th next year.

_______________

Rolling a 0 on a number cube Rolling a 0 on a number cube Impossible Impossible Rolling a number less than 3 on a number cube Rolling a number less than 3 on a number cube Unlikely Unlikely Rolling an even number on a number cube Rolling an even number on a number cube Equally likely Equally likely Rolling a number greater than 2 on a dice Rolling a number greater than 2 on a dice Likely Likely Rolling a number less than 7 on a number cube Rolling a number less than 7 on a number cube Certain Certain

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

Try 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 Probability: the probability of what should happen. It’s based on a rule: Theoretical Probability: the probability of what should happen. It’s based on a rule: # of favorable outcomes # of possible outcomes Example: Rolling a dice and getting a 3 = Example: Rolling a dice and getting a 3 =

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) 4/10 b)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

Independent: the outcome of one event DOESN’T effect the probability of another event Independent: the outcome of one event DOESN’T effect the probability of another event Example: Find the probability of choosing a green marble at random from a bag containing 5 green and 10 white marbles and then flipping a coin and getting tails. Example: Find the probability of choosing a green marble at random from a bag containing 5 green and 10 white marbles and then flipping a coin and getting tails. 5/15 x ½ = 5/30 = 1/6

Replacement: DOESN’T effect the probability of another event Replacement: DOESN’T effect the probability 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 = 5/48

Dependent: the outcome of one event DOES effect the probability of another event Dependent: the outcome of one event DOES effect the probability of another event 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 = 1/45

Without Replacement: DOES effect the probability of another event Without Replacement: DOES effect the 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 = 3/28

OR Probabilities: Add the probabilities OR Probabilities: Add the probabilities 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 = 1/3 Example 2: Choosing either an A or an E from the letters in the word mathematics. P(A or E) 2/11 + 1/11 = 3/11

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 Probabilities: Multiply the probabilities AND Probabilities: Multiply the probabilities 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?