# 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 your *experimental probability*?

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 your *experimental probability*?

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.