Probability

Contents 1. Introduction to probability terminology 2. Probability models to compare relative frequency of events with theoretical probability 3. Venn diagrams to solve probability problems.

Introduction to Probability The likelihood of an event happening is referred to as probability. The set of all the possible outcomes for an experiment is referred to as the sample space. CERTAIN EVENTS: these events will always happen. They have a definite outcome and a probability = 1. EVEN CHANCE EVENTS: these are They have a 50% chance of ocurring and a probability = ½. EQUALLY LIKEY EVENTS: each even has an equally likely chance of happening. IMPOSSIBLE EVENTS: these events can never happen. They have a probability =0

Probability Scale impossible Even chance (50/50) certain Probabilities are written as fractions, decimals or percentages. The less likely an even is to happen, the smaller the fraction. The greater the probability, the greater the fraction. 010,5 or ½

Calculating Probability When all outcomes of an even are equally likely, you can calculate the probability of the event ocurring by using the following formula: Eg: Suppose the you throw a dice. The possible outcomes are S = { 1,2,3,4,5,6}. If the even is {getting an even number}, then E{2;4;6}

Experimental vs. Theoretical Theoretical Probability is probability that can be determined by logical thought. Experimental Probability is determined through many trials. Only after many trials will the relative frequency get close to the theoretical frequency.

Venn Diagrams Venn diagrams represent a sample space and its events. Eg: Consider S= {1,2,3,4,5,6,7,8,9,10} Suppose that there are 2 events: C= {2,4,6,10} D = {2,6,8,9} The union of C and D: C u D ={2,4,6,8,9,10} The intersection of C and D: C n D = {2;6} Events with elements in common are called inclusive events. S CD