Counting The Number of Outcomes

​Counting the Number of Outcomes

By Saul Robles

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Objectives!

By the end of this lesson, students will be able to:

• Define outcome and sample space.

• Determine the number of possible outcomes using:

  • Lists/diagrams

  • The Multiplication Counting Principle

• a possible result of an action.

• ex: landing on heads when flipping a coin

Outcome

• the set/list of all possible outcomes.

• ex: S = {1,2,3,4,5,6}

Sample Space

• a visual tool used to list all possible outcomes of an event by branching out each choice step by step.

Tree Diagram

Find total number of Outcomes using a Tree Diagram and Sample Space.

1. How many outcomes are in a Quarter?

2. How many outcomes are in a six sided dice?

3. How many outcomes are in a spinner with four equal parts A, B , C, D?

4. What are the total number of outcomes in two Quarters?

5. How many outcomes total are there if you flip a coin and spin a spinner with 3 equal parts A, B, C?

Multiple Choice

How many possible outcomes are there when you spin the wheel of colors?

• 1

• 2

• 3

• 4

Multiple Choice

Which shows the sample space for flipping two coins? 
H = heads, T = tails

• H, T
• HH, HT, TH, TT
• HH, TT
• HH, TT, TT, HH

Multiple Choice

If the spinner is spun one time, how many possible outcomes are there?

• 1

• 2

• 8

• 64

Multiple Choice

What is the sample space when you roll a dice and then flip a coin?

• 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T

• 2

• 1,2,3,4,5,6,H,T

• if one action can occur in m ways and another in n ways, the total number of outcomes is m x n

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Multiplication Counting Principle

Find total outcomes using the Multiplication Counting Principle

• John has 3 shirts (Green, Blue, Red) and 2 pairs of pants (Jeans, Sweatpants). How many total outfit combinations can John make?

Multiple Choice

We have a spinner with 4 equal sections (A, B, C, D)

and a 6-sided Die. What is the total number of outcomes?

• 10

• 24

• 15

• 18

Fill in the Blanks

A deli offers the types of bread and sandwiches shown in the table. How many possible outcomes are there?

Multiple Choice

How many different outcomes?

• 7
• 9
• 8
• 5

Multiple Choice

Joleen is on a shopping spree.  She buys six tops, three shorts and 4 pairs of sandals.  How many different outfits consisting of a top, shorts and sandals can she create from her new purchases?

• 54
• 45
• 36
• 72

Conclusion

Review

• outcomes = possible results

• Sample Space = list of all outcomes

• Multiplication Counting Principle = easy way to find all possible outcomes without listing or using a tree diagram.