# Spinners and probability

## Same Spinners Same Numbers

If two spinners are divided equally, numbered with three numbers, will either spinner be more likely than the other to have higher or lower numbers?

Purpose: To investigate equal probability, unequal probability, experimental probability, theoretical probability, tree diagrams, and tables with respect to probability.

Materials: sets of equal spinners with like numbers and unlike numbers (spinners).

Procedure:

Determine:

• If two players use the same spinner (each spins a 1, 2, 3 spinner).
• Determine who would be more likely to spin the smaller or larger number in ten spins?
• Experimental probability: Find a partner and play ten games.
• Record the outcomes on the chart below: (1, 2, 3), and which person has the high or low number or tie.

Is it more likely to spin smaller numbers?

Would this be a fair game?

Why or why not?

Game data:

 Game 1 2 3 4 5 6 7 8 9 10 Total Spinner A 1 2 3 High, Low, Tie H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T __ H __ L ___T Spinner B 1 2 3 High, Low, Tie H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T H-L-T __ H __ L __ T

Share the data with the class and complete the class data chart.

Class data for 12 teams:

 Spinner A 1 2 3 Spinner B 1 2 3 Hight Low Tie High Low Tie Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 Team 8 Team 9 Team 10 Team 11 Team 12 Total

What is the class's experimental probability?

Theoretical probability: Use the tree diagram to determine all of the possible outcomes and record them in the chart below.

Possible outcomes tree:

 Spinner A 1 Spinner A 2 Spinner A 3 Spinner B 1 Spinner B 2 Spinner B 3

What is the experimental probability?

Hints

 Spinner A 1 Spinner A 2 Spinner A 3 Spinner B 1 1 1 tie 1 2 spinner A 1 3 spinner A Spinner B 2 1 2 spinner B 2 2 tie 2 3 spinner A Spinner B 3 3 1 spinner B 2 3 spinner B 3 3 tie

## Same Spinners Different Numbers

Purpose: To investigate equal probability, unequal probability, experimental probability, theoretical probability, tree diagrams, and tables with respect to probability.

Materials: sets of equal spinners with like numbers and unlike numbers (spinners).

Procedure

If two players use spinner divided into equal sections, but each has a different set of numbers on the spinner. Who would be more likely to spin the smaller or larger number in ten spins?

Experimental probability:

Find a partner and each spin one of the two different spinners (1, 5, 8 or 2, 4, 7) record the outcomes.

Is it more likely to spin smaller numbers?

Would this be a fair game?

Why or why not?

Game data:

 Game 1 2 3 4 5 6 7 8 9 10 Total spinner 1 5 8 High or Low H - L H - L H - L H - L H - L H - L H - L H - L H - L H - L ____ H - ____ L spinner 2 4 7 High or Low H - L H - L H - L H - L H - L H - L H - L H - L H - L H - L ____ H - ____ L

Share the data with the class and complete the class data chart.

Class data for 12 teams:

 Spinner 1 5 8 Spinner 2 4 7 High Low High Low Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 Team 8 Team 9 Team 10 Team 11 Team 12 Total

What is the class's experimental probability?

Theoretical probability: Use the tree diagram to determine all of the possible outcomes and record them in the chart below.

Possible outcomes tree:

 Spinner 158 - 1 Spinner 158 - 5 Spinner 158 - 8 Spinner 247 - 2 Spinner 247 - 4 Spinner 247 - 7

What is the experimental probability?

Hints

 Spinner 158 - 1 Spinner 158 - 5 Spinner 158 - 8 Spinner 247 - 2 2 1 spinner 247 2 5 spinner 158 2 8 spinner 158 Spinner 247 - 4 4 1 spinner 247 4 5 spinner 158 4 8 spinner 158 Spinner 247 - 7 7 1 spinner 247 7 5 spinner 247 7 8 spinner 158

How did you determine experimental probability?

How did you determine theoretical probability?

What is the difference between theoretical probability and experimental probability?

## Spinners

Use a paper clip to make a spinner.

• Put the smaller end at the center of the circle, so the larger end is toward the edge of the circle.
• Put the point of your pen or pencil inside the paper clip and on the center of the circle.
• Flick the paper clip so that it spins around the point.