Combinations of Outcomes How Many Possible Outcomes Are There???

Key Vocabulary Sample Space is the set of all possible outcomes. –It is shown most often as a list or a tree diagram.

Cup of Coffee Example Coffee Type: –Standard –Dark Roast –Light Roast –Decaffeinated –Half-caffeinated Sugar –None –Regular –Equal –Splenda –Sweet & Low Coffee Size –Short –Tall –Grande –Venti Milk –Nonfat –Lowfat –Regular –Half & half –Soy

Counting Principle We MULTIPLY the number of each option when ALL the options are possible. Thus, the Coffee problem results in 5 x 4 x 5 x 5 = 500 ways to have your coffee!

Clothing Example If I have 3 different shirts (red, blue, green), 2 pair of pants (black, grey) and can wear a hat or go hatless, how many outfits do I have?

Possible Outfits Red/Black/Hat, Red/Black/Hatless, Red/Grey/Hat, Red/Grey/Hatless Blue/Black/Hat, Blue/Black/Hatless, Blue/Grey/Hat, Blue/Grey/Hatless Green/Black/Hat, Green/Black/Hatless, Green/Grey/Hat, Green/Grey/Hatless This list is called the Sample Space, in this case we have 3 x 2 x 2 = 12 outfits in our Sample Space

Tree Diagram Green BlueRed Black Grey Hat Hatless HatHatless Hat HatlessHat If we count the bottom row, we will have the number of possible outcomes. In this case we have 12.

Homework Page 36, #1, 2 Page 40, #12 Page 41, #14, 15 Page 88, #30 Page 106, #3-7