Chapter 4 Section 1 Probability Theory

Section 1: What is probability? Probability of an Event ·     the likelihood of that event occurring ·     denoted P(A), A is the event ·     0 < P(A) < 1 ·     If an event is impossible, P(A) = 0 ·     If an event is a certainty, P(A) = 1

Experiment – any activity that yields a result or an outcome   Sample Space – the collection (or set) of all possible outcomes that can occur when an experiment is performed * when the experiment is performed, one and only one of these outcomes must occur  

Example Experiment: tossing a coin Outcomes: heads or tails Sample Space: S = {H,T}   Event – a collection (or set) of some of the possible outcomes from the sample space * an event is a subset of the sample space

Example Experiment: Tossing a die Sample Space: {1,2,3,4,5,6} Event: Rolling an even number = {2,4,6}

Probability formula for relative frequency P(A) = relative frequency = f/n  f is the frequency n is the sample size

Probability formula when outcomes are equally likely n(A) = number of ways A can occur n(S) total number of possible outcomes P(A) = P(A) or p – the probability that an event occurs   p + q = 1   P(A) or q – the probability that an event does not occur (complement) P(A) + P(A) = 1