Stats and Probability

• An event which is impossible has a probability of 0 and an event which is certain has a probability of 1. This means probabilities cannot be bigger than 1.
• p(event)=outcomes matching event/total outcomes
• Events that cannot happen at the same time are called mutually exclusive events. For example, a football team can win, lose or draw but these things cannot happen at the same time. Since it is certain that one of these outcomes will happen, their probabilities must add up to 1.
• Combinatorics is the number of ways of arranging something.
• Theoretical probability


  When we know the underlying probability of an event.
• Experimental probability/relative frequency


  A probability based on observing counts. p(event)=count of outcome/number of trials. Used to estimate probability when theoretical probability cannot be used.
• Combined events can be shown in different ways such as by systematic listing, or by using tables, grids, Venn diagrams, the product rule and tree diagrams. The probability of a particular combined event can then be found.
• Systematic listing


  The outcomes for an event can be listed in an organised or systematic way to make sure that none of the possible outcomes is missed out. Look for patterns to help find all the outcomes.