Transcript: HARD!! You are off the soccer, and love eing the goalkeeper, but that depends who is the Coach today. With coach Sam the probability of being a goalkeeper is 0.5. For Coach Alex the probability is 0.3. Coach Sam is more often about 6 out of 10 every game. So whats the probability of being a goalkeeper today? 0.6 x 0.5 = 0.3 0.4 x 0.3 = 0.12 0.3 + 0.12 = 0.42 So the probability of 2 numbers less than 5 is 4/9 Probability So the probability of being a goalkeeper today is 0.42 Question 1 Answer 2 = numbers of favorable outcome/total number of possible outcome Answer 1 Keywords 1. Draw the tree diagram 2. Calculate along the branches 3. You get the probability!! We use tree diagram for calculating the PROBABILITY Two dice are thrown together. Use a tree diagram to calculate the probability that both numbers are less than 5 How to calculate? Question 2 _ _ _ _ _ _ _ _ _ _ _ Random - without definite aim Replaced - to be used instead of Independent - not relying on something else Conditional - implying on a condition Event - the final outcome TREE DIAGRAM A Song for Probability
Transcript: How confident do you feel with this topic? Write Red, Amber or Green in your books. What is the probability of getting a bead of each colour? Confident.... When you flip a coin, there are two outcomes. You can get a head or a tails. Create a tree diagram showing the possible outcomes of flipping a coin 3 times ½ Bag A contains three red marbles and four blue marbles. Bag B contains five red marbles and three blue marbles. A marble is taken from each bag in turn. Find the missing probabilities for the tree diagram ½ Probability Tree Diagrams Continued.. Probability Tree H T Starter LO: Developing students will be able to add probabilities for mutually exclusive events Secure students will be able to work out the probability that something will not happened given that you know the probability that it will happen There are 8 possible outcomes! The sum for the probability of any branch is always 1! •Estimate the number of times an event will occur Objective Tree Diagram Developing students will be able to use a tree diagram to work out probability Secure students will be able to Question To find a probability of an outcome we multiply along the branches and add vertically! Question Probability tree diagram shows all possible outcomes of an experiment What is the probability of getting a blue bead followed by a red? What is the probability of getting a blue bead followed by a red? What is the probability of getting a bead of each colour? 1st Flip 2nd Flip 3rd Flip The probability of three heads is: P (H H H) = 1/2 × 1/2 × 1/2 = 1/8 ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½ ½ H T ½
Transcript: WHERE TORNADOES OCCUR THE DAMAGE COST tornadoes have on humans is the property damage. Weak tornadoes can take the roofs off buildings and break windows. Stronger tornadoes have been shown to level buildings. This can have a considerable economic impact. In 1999, Oklahoma suffered about $1.1 billion in property damage and crop losses from tornadoes The intense spinning of a tornado is partly the result of the updrafts and downdrafts in the thunderstorm (caused by the unstable air) interacting with the wind shear, resulting in a tilting of the wind shear to form an upright In the USA over 26 percent of tornadoes are dangerous but when 76 percent are weak there is still a high chance of people getting hurt HOW MANY TORNADO EFFECT US ornadoes effect the environment by destroying buildings anTd trees. Tornadoes also kill animals, which effects the food chain and disrupts the whole environment. Tornadoes destroy our farms, which means there will be food shortages around the surrounding area. After everything is destroyed, humans have to rebuild. Tornadoes can cause water contamination, which poses a serious problem, as plants, animals and humans are effected by this. Debris can be very dangerous, as it could kill plants and animals very easily. EFFECT A tornado is destructive vortex of violently rotating winds having the appearance of a funnel-shaped cloud and advancing beneath a large storm system. when do tornadoes occur? Tornadoes can happen every day they just have to depend on air and weather tornado season is usually May, April and June. TREE DIAGRAM CAUSE Most tornadoes occur in the deep south and broad,relatively flat basin between the Rockies and the Appalachians, but no state is immune. Peak months of tornado activity in the U.S. are April, May, and June.At the core of Texas there is a place called tornado alley, this is where tornadoes happen most frequently. TORNADO
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Transcript: You are at a carnival. One of the carnival games asks you to pick a door and then pick a curtain behind the door. There are 3 doors and 4 curtains behind each door. How many choices are possible for the player? -Easier to visually make the connection between the diagram and the underlying probability concepts using tree diagrams -Tree diagram makes conditional probability easier to be understand. Dependent event (Conditional event) Independent event -Conditional events are things that depends on what happened before Therefore another name for conditional event is dependent event. e.g.taking colored marbles from a bag: as you take each marble there are less marbles left in the bag, so the probabilities change. How to build your tree diagram 1. List all the possible choices 2.Branch off the possible choices with more possible choices 3.Branches are determined by the number of combinations you will have. -In probability tree diagrams are used to represent a probability space. -Tree diagrams represents a sires of independent events or conditional events Example Problem - Independent events are events that are not affected by previous events. e.g.A coin does not "know" it came up heads before, so each toss of a coin is a perfect isolated thing. Advantages of tree diagram Introduction Tree Diagram
Transcript: Probability Edition Extra "And" Means Multiply Examples Real life application Tree diagram are found in most of our lives. We use tree diagram to find all of the possible outcome. Reference http://www.regentsprep.org/regents/math/algebra/apr4/practre.htm http://www.mathsisfun.com/data/probability-tree-diagrams.html Math Make Sense Text book http://nrich.maths.org/7288 Instruction You removed all of the 4 aces from a deck (ace of diamond, ace of clovers, ace of hearts and ace of spades). A coin is tossed and one of the aces are chosen. What are the chances of getting heads and an ace of spades? Example 1 1/6. What is a tree diagram Answer is.... To do this question, you must do a tree diagram to find all of the outcome. A tree diagram is a diagram that resembles branches of a tree, it is used for listing all the possible outcomes. 1/8 Should look something like this. The answer is.... Tree diagram By Jeff Example #2 To build an Tree diagram you have to find all of the possibility. You then start off with the beginning and then branch off to the other possibilities. Depending on the amount of possibilities that are in the question. You are rolling a dice 6 sided. What are the percent possibility of each out come? "Or" Means Add
Transcript: An Action Plan - Specialized knowledge is usually required The Tree Diagram takes the key issues from the other exercises and "explodes them down to the lowest practical level of detail" - Makes sure all bases are covered and that the "lines of logic" are sound - Good to use for: - a specific task (but not a simple assignable job) - a task with complex implementation - when a simple task has run into repeated roadblocks in implementation Tree Diagram Detail 4 How does it relate to Affinity and Interrelationship Digraph? Construction of a Tree Diagram Detail 3 1. Choose the Tree Diagram Goal Statement This tool systematically maps out in increasing detail the full range of paths and tasks that need to be accomplished in order to achieve a primary goal and every related subgoal. Can come from three sources: 1. The Interrelationship Digraph (core/secondary issue) 2. The Affinity Diagram (usually a header card + the cards under it) 3. Original Issues (most common) Detail 1 Pure Linear Logic Detail 2 Definition 2. Assemble the Right Team 3. Generate the Major Tree Headings
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