* forecasting, hazard assessment, error analysis, recurrence interval, radioactive decay
*

**Geologic context:**# Understanding odds and probability in the geosciences

^{by Dr. Eric M. Baer, Geology Program, Highline Community College}

*Jump down to:*Teaching strategies | Materials & Exercises | Student Resources

The probability (

**P**) of a favorable outcome is

_{f}-
### P

_{f}= f/n

**where:****n**is the total number of possible outcomes and**f**is the number of possible outcomes that match the favorable outcome criteria.

## Teaching Strategies: Ideas from Math Education

### Put quantitative concepts in context

- Hazard assessment including earthquakes, floods , and volcanic eruptions
- Extinctions and extinction rates
- Error and data analysis including uncertainty and error propagation
- Forecasting

### Use multiple representations

**Verbal representation**

**Numerical representation**

- ratio - written as 1:3 or 1 in 3.
- fraction - 1/3 or sometimes even as an unreduced fraction 3/9
- percentage - 33%
- decimal - 0.33

**Tabular representation**

Sum | probability (fractional) | probability (percentage) |

2 | 1/36 | 2.78% |

3 | 2/36 | 5.56% |

4 | 3/36 | 8.33% |

5 | 4/36 | 11.11% |

6 | 5/36 | 13.89% |

7 | 6/36 | 16.67% |

8 | 5/36 | 13.89% |

9 | 4/36 | 11.11% |

10 | 3/36 | 8.33% |

11 | 2/36 | 5.56% |

12 | 1/36 | 2.78% |

TOTAL | 36/36 | 100% |

**Graphical representation**

There are several graphical ways to portray both probabilities and probability distributions.

**Graphical ways of showing probabilities**

**Graphical ways of showing probability distributions**

**Model representation**

Chance/probability of death from various causes for an average American in a given year.

Cause of death | Probability |

Aids/HIV infection | 1 in 19,000 |

Airplane Crash | 1 in 2,736,000 |

Alcoholic Liver Disease | 1 in 22,000 |

Car Crash | 1 in 6357 |

Earthquake | 0 to 1 in 40,000,000 |

Falls | 1 in 20,688 |

Flood | 1 in 6,700,000 |

Food Poisoning | 1 in 53,000 |

Heart disease | 1 in 387 |

Homicide | 1 in 16439 |

Suicide | 1 in 9350 |

**Algebraic representation**

**P**) of a favorable outcome is

_{f}-
**P**_{f}= f/n

**n**is the total number of possible outcomes and

**f**is the number of possible outcomes that match the favorable outcome criteria.

### Use technology appropriately

Students have any number of technological tools that they can use to better understand quantitative concepts -- from the calculators in their backpacks to the computers in their dorm rooms. Probability and recurrence intervals can make use of these tools to help the students understand this often difficult concept.

- Graphing calculators
- Computers

### Work in groups to do multiple day, in-depth problems

Mathematicians also indicate that students learn quantitative concepts better when they work in groups and revisit a concept on more than one day. Therefore, when discussing quantitative concepts in entry-level geoscience courses, have students discuss or practice the concepts together. Also, make sure that you either include problems that may be extended over more than one class period or revisit the concept on numerous occasions.

Probability is a concept that comes up over and over in introductory geoscience: Volcanic eruptions, mass extinctions, earthquakes, floods, confidence intervals, etc. When each new topic is introduced, make sure to point out that they have seen this type of mathematics before and should recognize it.

## Teaching Materials and Exercises

**Determining Earthquake Probability and Recurrence**

**Is there a present volcanic hazard?**

**Chance news (more info)**

**Texas instruments activity page**

**The Math Forum (more info)**