1. Discrete Math 6-1 Copyright © Genetic Computer School 2007 Lesson 6 Probability

2. Discrete Math 6-2 Copyright © Genetic Computer School 2007 Lesson 6 Overview Basic concepts of probability theory Relative frequency and probability Defining probability Combining probabilities Either... Or... Probability tree

3. Discrete Math 6-3 Copyright © Genetic Computer School 2007 Basic concepts of probability theory Probability Any particular stated probability is an assertion that indicates how likely you believe it is that an event will occur. We can express the probability of an event mathematically as a decimal between 1 and 0. Thus, a probability of 1 (p = 1) is certainty that the event will occur. A probability of 0 (p = 0) is certainty that event will not occur. Thus, all probabilities for an event are expressed as a decimal between 0 and 1

4. Discrete Math 6-4 Copyright © Genetic Computer School 2007 Relative frequency and probability Relative frequency measures how one particular class occupies the distribution as a whole and in what proportion. So it gives the probability for each class. The phrase "chosen at random" means that all items are equally likely to be chosen

5. Discrete Math 6-5 Copyright © Genetic Computer School 2007 Defining probability If the possibility space S consists of a finite number of equally likely outcomes, then the probability of an event E, written P(E) is defined as n(S): Number of sample points in the possibility space n(E): Number of sample points in the event space

6. Discrete Math 6-6 Copyright © Genetic Computer School 2007 Combining probabilities Events can sometimes be the results linking two or more events in some way. The resulting events are then called compound events. This type of probability involves two (or more) events which must happen at the same time. It can be described as ".. both event A and also event B..".

7. Discrete Math 6-7 Copyright © Genetic Computer School 2007 Either... Or... Two events taking place, but not necessarily both. In words, it will be "... either event A or event B..."

8. Discrete Math 6-8 Copyright © Genetic Computer School 2007 Probability tree