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Probability

Probability. Tree Diagrams Friday, September 9, 2011 Mr. Pearson. What are Tree Diagrams?. A way of showing the possibilities of two or more events Simple diagram we use to calculate the probabilities of two or more events

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Probability

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  1. Probability Tree Diagrams Friday, September 9, 2011 Mr. Pearson

  2. What are Tree Diagrams? • A way of showing the possibilities of two or more events • Simple diagram we use to calculate the probabilities of two or more events • Tree diagrams show you the outcomes that are possible while the Fundamental Counting Principle only tells you how many are possible, not the actual outcomes.

  3. Using the fundamental counting principle we can figure out how many ways to order a pizza. Suppose your favorite pizza place had a special for a 1-topping pizza with the following options: Because the size, type of crust, and topping are all independent events, we can use the fundamental counting principle to determine how many different choices of pizza we could make. number of pizzas = 3 sizes  • 2 crusts • 4 toppings = 3 • 2 • 4 = 24 possibilities

  4. Possible Outcomes For example – a fair coin is spun twice 1st 2nd H HH H T HT H TH T T TT

  5. Shows all possible outcomes Total amount of choices from a group of items How many of a particular item out of all the possible choices Tree Diagrams

  6. 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 5 1 2 3 4 5

  7. 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 item There are 3 options: Red White Blue

  8. 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. 1 2 3 4 5

  9. 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. 1 2 3 4 5 R W B R W B R W B R W B R W B

  10. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue • Go to the last column of the tree diagram and count how many options are listed. 1 2 3 4 5 R W B R W B R W B R W B R W B

  11. PROBLEM: How many options are there of picking a number from 1 to 5 and choosing the color red, white, or blue • There are a total of 15 total choices listed

  12. PROBLEM: What is the chance of choosing the color red? • There are five different times the color red could be chosen from all 15 options • The chance of having the color red is 5/15 or reduced is 1/3

  13. Your turn!Please do on your own paper. 1. Give the total number of outcomes of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram. 2. What is the chance of having a hot dog? Write in fraction form. H E L P!

  14. PROBLEM: 1.Give the total number of outcomes of choosing a hamburger, hot dog, or chicken and potato salad, coleslaw, or beans. Use a tree diagram. • Answer: Hamburger Hot dog chicken potato salad coleslaw beans potato salad coleslaw beans potato salad coleslaw beans

  15. PROBLEM: 2. What is the chance of having a hot dog? Write in fraction form. • Answer: • First find out how many total options there are. Here there are a total of nine choices. This is your denominator. • Next find out how many options have a hot dog. Here there are a total of three choices. This is your numerator. • Finally, put the fraction in simplest form. • The answer is 3/9 and then simplified is 1/3 STOP

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