#### Research & Analysis

**Reference data**

- Remote Sensing Systems (Earth Geophysical Microwave Data)
- National Snow and Ice Data Centre
- Historical Carbon Dioxide Record from the Vostok Ice Core
- Atmospheric Carbon Dioxide – Earth System Research Laboratory
- NOAA National Centre for Environmental Information
- Centre for Ice and Climate

**Research community **

In the field of Safety Engineering, probabilistic and deterministic mathematical representations are used to calculate how likely an event may occur, which could lead to a major hazard. Although there are several different interpretations, probability theory treats the concept in a rigorous mathematical manner, by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of these outcomes is called an event.

**1. Basic theoretical probability**

- Introduction to theoretical probability
- Probability the Basics
- Simple Probability: yellow marble
- Simple Probability: none blue marble
- Intuitive sense of probabilities
- The Monty hall problem

**2. Probability using sample spaces**

- Probability with counting outcomes
- Example: all the ways you can flip a coin
- Die rolling Probability
- Subsets of samples spaces

**3. Basic set operations**

- Intersection and union of sets
- Relative complement or difference between sets
- Universal set and absolute complement
- Subset, strict subset, and superset
- Bringing the set operations together

**4. Experimental probability**

- Experimental Probability
- Theoretical and experimental probabilities
- Making Predictions with probability
- Simulation and randomness

**5. Randomness, probability, and simulation**

#### Cont.

**6. Additional rule**

**7. Multiplication rule for independent events**

- Sample spaces for compound
- Compound probability of independent events
- Probability of a compound event
- Coin flipping probability
- Free-throw probability
- Three-pointer vs free-throw probability
- Probability without equally likely events
- Independent events example, test taking
- Die rolling probability with independent events
- Probabilities involving ‘at least one’

**8. Multiplication rule for dependent events**

- Dependant probability introduction
- Dependant probability, coins
- Dependant probability example
- Independent & Dependant probability
- The general multiplication rule
- Dependant probability

**9. Conditional probability and independence**

- Calculating conditional probability
- Conditional probability explained visually
- Conditional probability using two-way tables
- Conditional probability tree diagram: example
- Tree diagrams and conditional probability
- Conditional probability and independence 1
- Conditional probability and independence 2
- Analyzing event probability for independence