Unit 6: Probability - Lesson 6

Unit 6: Probability

Lesson 6 - Compound Events --Long Version

Outcomes = Combinations

• When given options, think of ALL the combinations that you can create!

• Ex: 1 belt, 3 shirts, and 2 pants

• How many different combos can you make?

Multiple Choice

James has 3 shirts [red, yellow, green], 1 belt, and 2 pants [blue and khaki]. How many different combinations can you create that has a belt included?

• 3

• 6

• 9

• 12

Multiple Select

Aimee wants to pack enough items for 6 different outfits. She packs 1 jacket, 3 shirts, and 2 pairs of jeans. Select ALL the possible outcomes:

• Jacket, Shirt 1, Pant 3

• Jacket, Shirt 3, Pant 1

• Jacket, Shirt 2, Pant 2

• Jacket, Shirt 1, Pant 2

• Jacket, Dress 1, flats 2

Compound Events

Compound Events: consists of 2 or more simple events.

You can use organized lists, tables, or tree diagrams to see all outcomes.

Often times, making a tree diagram is the best choice to see all the combinations possible.

Multiple Choice

Adrienne, Carlos, and Greg are chosen to represent Mr. Baldrick's class in a school assembly on stage. How many different combinations can they sit in a row on stage?

• 3

• 1

• 9

• 6

Multiple Select

Adrienne, Carlos, and Greg are chosen to represent Mr. Baldrick's class in a school assembly on stage. Select ALL possible outcomes:

• ACG AGC

• CAG CAA

• CGA CAG

• GAC GCA

Remember

• There are many combinations that you can make that are unique and different.

• For Example: 5 students swam in a race: Abby, Carlos, Harry, Peter, and Zane. Their order of finishing the race is important.

Multiple Select

You are buying a car from the dealership. There are 2 car types [sedan or hatchback]; 5 colors [grey, red, green, dark blue, or light blue], and 3 types of models [GL, SS, or SL]. Select ALL possible outcomes from the items listed.

• Hatchback grey GL

• Hatchback grey LX

• Light Blue Sedan SS

• Sedan Red GL

• White Sedan LX

Determining Probability of Compound Events

• The probability of a compound event, just as with simple events, is the fraction or ratio of outcomes in the sample space in which the compound event occurs.

Being Specific with Probability

When determining probability, sometimes we want a specific thing to happen.

Ex: Probability of getting [HHH] exactly when you toss 3 coins.

Multiple Choice

What is the probability of tossing 3 coins and getting [tails, tails, tails]? Or P(3 Tails) = ?

• 1 / 4

• 1 / 8

• 1 / 3

• 1 / 6

"AND" = Multiply

• When probability wants specific events, we use the term AND

• This means that one event will happen AND another event will happen.

• Ex: Probability of rolling a pair of dice and landing on 2 and 3 [or sum of 5]

• P(2 and 3) = P(2) x P(3)

Multiple Choice

Alana tosses 2 number cubes. She wins if she rolls double sixes. Determine P(Alana wins) or P(6 and 6).

• 2 / 6

• 1 / 3

• 1 / 36

Applying the Fundamental Counting Principle to Compound Events

• Ex: A Ice cream shop has 5 ice cream flavor options, 2 cone options, and 3 toppings options. How many total outcomes or combinations are there?

• Multiply Each option type:

• Ice Cream Flavors x Cone Types x Topping Type

• 5 x 2 x 3 = 30 total Outcomes

Multiple Choice

Hannah is trying to determine the total number of outcomes she can get if she: tosses a coin 2 times, and rolled a number die.

• 2 x 2 x 6 = 24

• 2 x 6 = 12

• 2 x 2 + 6 =10

• 2 + 2 + 6 = 10

You can use the F.C.P. with Passwords!

• Ex: Carl is given a password that is 4 digits long, each number is between 1 and 4. There can be NO repeating numbers.

• 1st number has 4 outcomes

• 2nd number has 3 outcomes

• 3rd number has 2 outcomes

• 4th number has 2 outcomes

• 4 x 3 x 2 x 1 = 24

Multiple Choice

Kamrin has designed a password for her phone that consists of 1 capital letter, followed by 2 numbers [each between 0 and 9] and a lower case letter. What is the total number of combinations that she can create? There can not be any repeating letter or number.

• 26² x 10²

• 26 x 9² x 25

• 26 x 25 x 10 x 9

Multiple Choice

Kamrin has designed a password for her phone that consists of 1 capital letter, followed by 2 numbers [each between 0 and 9] and a lower case letter. What is the total number of combinations that she can create? Repeating letters or number are allowed.

• 26² x 10²

• 26 x 9² x 25

• 26 x 25 x 10 x 9

Poll

• 1. I don't understand, and I need help.

• 2. I understand this a little, but I'm still a little confused.

• 3. I understand this.

• 4. I understand this, and I could teach it to someone else.