2 Important Probability Terms EventOutcomeProbabilitySample SpaceCompound EventsIndependent EventDependent EventTree Diagram Organized ListCounting PrincipleExperimental ProbabilityTheoretical Probability
3 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 happenThere is a strong chance it’ll happenIt’ll definitely happen!!!It’ll NEVER happen!!!
4 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 = 1P = 0P = 0.25P = 0.5P = 0.75It is not very likely it’ll happen.It might happenThere is a strong chance it’ll happenIt’ll definitely happen!!!It’ll NEVER happen!!!
6 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.
7 Probability What is probability? The likelihood of an event occurring. What are the odds of flipping a coin and landing on heads?
8 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 aretwo possible outcomesP (event) =Number of favorable outcomesTotal number of possible outcomes
9 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 occursTotal number of experiments
10 Experimental Probability P (event) =Number of times an event occursTotal number of experimentsEvent = scoring a basket21131Number of baskets scoredNumber of shots taken
11 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.TheoreticalExperimentalExperimentalTheoretical
12 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?
13 Another ExampleIf 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?
14 Your TurnIf you rolled a six sided die, what is the probability that you would roll and even number?A. 1/6 C. 6/6B. 2/6 D. 1/2
15 Try AnotherA 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. 3/5B. 6/30 D. 12/30
16 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 outcomesNumber of total outcomes=
17 An Example If you were to spin this spinner, what would the probability be of landingon bankrupt or lose turn?P (bankrupt or lose turn)
18 Another ExampleA 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?
19 Your TurnWhat is the probability of picking a card out of a standard deck and drawing a jack or 4?A. C.B. D.
20 Try AgainWhat is the probability of picking a card out of a standard deck and drawing a queen, king, or jack?A. C.B. D.
21 HomeworkProbability Worksheet PLEASE SHOW YOUR WORK!! No homework passes for this assignment! (Sorry)
22 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?
23 Tree DiagramsShows all possible outcomes in anorganized drawing.
24 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 512345
25 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 itemThere are 3 options:RedWhiteBlue
26 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 3.12345
27 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.12345RWBWhat is the chance of choosing the color red?RWBRWBRWBRWB
28 PROBLEM: What is the chance of choosing the color red? There are five different times the color red could be chosen from all 15 optionsThe chance of having the color red is 5/15 or reduced is 1/3
29 Let’s TryHow many combinations of sandwiches can you make with the following options?Types of Bread Fillings*Wheat *Cheese*Italian *Ham*Rye *Turkey*Salami
30 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.
31 Organized ListsAnother 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?
33 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 = 10List: red 1, red 2, red 3, red 4, red 5, blue 1, blue 2, blue 3, blue 4, blue 5
34 Try the ShortcutHow many combinations can you have with 3 colors and 10 numbers?A C. 30B D. 7
35 Try the ShortcutHow many combinations are in a sample space with rolling 2 dice and tossing a coin?A C. 12B D. 36
36 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.
37 Independent EventsTwo 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.
38 Independent EventsMultiplication Rule : When two events, A and B, are independent, the probability of both occurring is: P(A and B) = P(A) · P(B)
39 Independent EventEach spinner is divided into equal sections. The two spinners are spun together . What is the probability of landing on blue and an even number?
40 Another ExampleA 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.
41 Your TurnA 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.
42 Try againWhat is the probability of rolling an even number on a die and tossing a coin and landing on tails?A. 1/2 C. 1/4B. 1/8 D. 2/3
43 Dependent EventsTwo 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?
44 Another ExampleMr. 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?
45 Your TurnThree 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.
46 Another TryIn 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. 2/650B. 6/325 D. 2/3
47 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?