In a random sample, each case has an equal chance of being selected. So, we can use probability theory to calculate how likely it is that our sample represents the population. Probability theory is the foundation of inferential statistics. Inferential statistics: calculations aimed at generalizing findings from our sample to the population. 0 is certainty it will not occur, 1 is certainty it will occur. Commonly we express the chance of an event as a percentage or a fraction. As a percentage (e. g. p=1 is a chance of 100%, and p=0. 5 is a chance of 50%) As a fraction (e. g. p=0. 25 is a chance of 1 in 4, and p=0. 01 is a chance of 1 in 100. Odds are much different and are often used in gambling and are misleading on purpose. Probability distribution: similar to a frequency distribution but it expresses probabilities. Key distinction in inferential statistics is the difference between theoretical and empirical probabilities.