pencil, highlighter, GP notebook, textbook, calculator Start working on IC – 1 from your textbook. Suppose that you were going to flip three coins: a penny, a nickel, and a dime. IC – 1 a)Make an organized list that shows all the possible outcomes. This list of all the possible outcomes is known as the sample space for this experiment. b) How many outcomes are there? c) What is the probability of flipping: i) three heads?ii) at least 2 heads? iii) 1 head and 2 tails?iv) at least 1 tail? v) exactly 2 tails?vi) at least 1 head and 1 tail? total:

Suppose that you were going to flip three coins: a penny, a nickel, and a dime. IC – 1 a)Make an organized list that shows all the possible outcomes. This list of all the possible outcomes is known as the sample space for this experiment. HHH sample space: HHT HTH HTT TTT TTH THT THH b) How many outcomes are there? 8 outcomes +2 +1

IC – 1 c) What is the probability of flipping: HHH sample space: HHT HTH HTT TTT TTH THT THH d) Which is more likely: flipping at least 2 heads or at least 2 tails? Explain your answer. P (at least 2 heads) = i) three heads?ii) at least 2 heads? iii) 1 head and 2 tails?iv) at least 1 tail? v) exactly 2 tails?vi) at least 1 head and 1 tail? P (at least 2 tails) = Neither is more likely to happen over the other. +2 total:

IC – 1 e) Remember that one way to create an organized list to represent this sample space is to make a tree diagram. The first coin, the penny, can either come up heads or tails. From there, we show the possible outcomes as branches. If you did not do so already, represent this sample space as a tree diagram. penny HT HTHT HTHTHTHT nickel dime

IC – 2 You have decided to take a vacation. You want to go from Los Angeles to San Francisco and then to Hawaii, and you have all summer for your trip. To get from Los Angeles to San Francisco you can choose to drive, fly, take a bus, or take the train. From San Francisco to Hawaii you can fly, cruise, or sail. a) Make a tree diagram to represent the possible choices in this problem. LA to SF drive fly bustrain cruisesailflycruisesailflycruisesailflycruisesail SF to Hawaii

IC – 2 b) How many choices do you have for the first leg of your trip? How many for the second? There are 4 choices for the first leg of the trip. There are 3 choices for the second leg of the trip. c) In how many different ways can you travel from Los Angeles to Hawaii? There are 12 different ways can you travel from Los Angeles to Hawaii. d) If you randomly choose your means of transportation, what is the probability of flying both times? P (flying both times) =

IC – 3 While playing Scrabble ®, you need to make a word out of the letters A N P S. a) How many arrangements of these letters are possible? ANPS ANSP APNS APSN ASNP ASPN NAPS NASP NPAS NPSA NSAP NSPA PANS PASN PNAS PNSA PSAN PSNA SANP SAPN SNAP SNPA SPAN SPNA There are 24 total arrangements. b) Of those arrangements, how many are words? What are they? There are 4 words. c) What is the probability of a two–year–old randomly making a word using the four letters? P (actual word) =

IC – 4 a) Try to make a list (sample space) of the possibilities. What is the difficulty here in trying to create a sample space? A typical counting problem might read: "How many four–digit numbers can be made using the digits 1, 2, 3, 4, 5, 6, 7 if it is okay to repeat a digit in a number?" In order to solve this problem, you could take a variety of approaches Etc. There are way too many possibilities to list.

IC – 4 Try to make a tree diagram for this problem. What is the difficulty here in trying to make a tree diagram? 1 st digit There are way too many branches to show.

IC – 4 b) A better method for organizing this problem is to condense it into a decision chart. Start by asking, "How many decisions (or choices) do I need to make in this problem?" In this case, the problem asks for four–digit numbers so there are four decisions. You can set up a chart for the four decisions as follows: 1 st digit2 nd digit3 rd digit4 th digit c) How many choices do you have for the first digit?7 7 d) The problem states that it is okay to repeat digits. What does that imply? At each decision there are 7 choices. There are 7 choices for each digit. e) How many choices do you have for the second digit? the third? the fourth? Visualize a tree diagram. 777

IC – 4 1 st digit2 nd digit3 rd digit4 th digit 7777 f) Explain how to find the answer to the original question. Justify your reasoning. Multiply together the total choices for each digit. 7  7  7  7 = 2401 There are 2401 four–digit numbers. Isn’t a good thing we didn’t finish the tree diagram?

IC – 5 Refer back to the Scrabble ® problem. Make a decision chart for that problem 1 st letter 4 2 nd letter 3 3 rd letter 2 4 th letter 1 There are 4 letters, A N P S, to choose from for the 1 st letter. Once a letter – any letter – is chosen for the first position, then there are 3 letters left to choose from for the second position. Now that the first two positions are filled, then there are 2 letters left for the 3 rd position. Finally, since the first three positions are filled, then there is only 1 letter left for the 4 th position.  = 24

Work on IC – 6 and IC – 7 in your groups.

IC – 6 1 st digit 7 2 nd digit 6 3 rd digit 5 4 th digit 4 There are 7 numbers to choose from for the 1 st digit. Once a number – any number – is chosen for the first digit, then there are 6 numbers left to choose from for the second digit. Now that the first two digits are filled, then there are 5 numbers left for the 3 rd digit. Finally, since the first three digits are filled, then there are 4 digits left to choose from for the 4 th digit.  = 840 Make a decision chart to help you answer the following question: "How many four–digit numbers could you make with the digits 1, 2, 3, 4, 5, 6, 7 if you could not repeat the use of any digit?"

Use decision charts to answer parts (a) and (b) then explain the similarities and differences in the two situations. IC – 7 a) A child's game contains nine discs, each with one of the numbers 1, 2, 3,..., 9 on it. How many different 3–digit numbers could be formed by choosing any three discs? 1 st digit 9 2 nd digit 8 3 rd digit 7  =

IC – 7 b) A new lotto game called Quick Spin has three wheels, each with the numbers 1, 2, 3,..., 9 equally spaced around the rim. Each wheel is spun once and the number the arrow points to is recorded. How many three digit numbers are possible? 1 st digit 9 2 nd digit 9 3 rd digit 9  =

Finish the assignment: IC 8 – 13, 15, 16