6th Grade Math Textbook, Fundamentals

• Francisco spins this spinner, which is divided into 3 equal sections.
  How many elements are in the sample space? List the sample space.
  Sample space {7, 9, 11}
  There are 3 elements in the sample space.


• Suppose Francisco spins the spinner twice.

Which possible outcome is more likely: that the sum of the spins

equals 18 or that the sum will not be 18?

Use a tree diagram to identify the sample space.

Notice that the tree diagram gives all the possible

outcomes for this experiment.

Sample space {(7, 7); (7, 9); (7, 11); (9, 7); (9, 9); (9, 11); (11, 7); (11, 9); (11, 11)}

There are 9 outcomes in the sample space, and 3 of these outcomes are sums of 18.

So since there are 6 outcomes that are notsums of 18, a sum that is not18 is more

likely to occur than a sum of 18.

Another way to find a sample space is to make an organized list or table.

Frank flips two nickels at the same time.

What is the sample space for this experiment?

Each nickel will land heads up (H) or tails up (T).

The table at the right shows the possible combinations.

Sample space {HH, HT, TH, TT}

So there are 4 possible outcomes in the sample space.

Spin 1 Spin 2 Outcome Sum of Numbers

7 7 {7, 7} 14

7 9 {7, 9} 16

711{7, 11} 18

9 7 {9, 7} 16

9 9 {9, 9} 18

9 11 {9, 11} 20

11 7 {11, 7} 18

11 9 {11, 9} 20

11 11 { 11 , 11 } 2 2

Spin 1 Spin 2

7

9

11

7

7

9

11

9

7

9

11

11

Practice & Activities

Lesson 12-1 for exercise sets. Chapter 12 331

Draw a tree diagram or make a table to find the number of possible outcomes.
List the sample space. (Note: A number cube has a different number from
1 to 6 on each of its six faces.)

1.Ian tosses a number cube twice. 2.Jan flips a nickel and spins the spinner

at the top of the page.

3.Discuss and Write Is Ian more likely to roll an even sum or an odd sum?

Support your answer with a diagram.

711

9

Nickel 2

HT

HHHHT

TTHTT

Nickel

1