[size=150]Introduction to Independent Events, Product Spaces, and the Binomial Density:[br][br]Two events are defined as independent events, if the outcome of one event does not affect the probability of the outcome of the other event. [br][br]By using an extension of the conditional probability formulas introduced previously,[br]P(A|B) = P(A ∩ B) / P(B) and P(B|A) = P(A ∩ B) / P(A) [br][br]can be manipulated to show the Multiplication rule for the probability of events A and B,[br]P(AnB) = P(A|B)*P(B) and P(AnB) = P(A)*P(B|A) [br][br]and derive the formula for independent events to become P(AnB) = P(A)*P(B) [br][br]For a given process, let S be the set of all possible outcomes. A and B are subsets (events) contained in set S. Therefore, for independent events A and B, the P(AnB) = P(A)*P(B) [br][br]The binomial density formula is used to calculate the probability of a certain number of successes in a fixed number of independent trials. [br][br]Binomial Distribution Formula P(X = r) = nCr*P(success)^r*P(failure)^(n-r)[br]Where P(success) + P(failure) = 1[br][br]Use Probability Density Bar chart to display corresponding binomial distribution[br][br]Questions students should be able to answer:[br]1) What is the probability of the first event?[br][br]2) How to determine if two events are independent?[br][br]3) When can the Binomial Distribution Formula be used?[br][br]4) How to create a Probability Density Bar chart?[/size]