m16848 Probability Topics: Venn Diagrams (optional) 1.9 2008/05/27 16:55:38 GMT-5 2009/02/19 17:44:21.423 US/Central Susan Dean Susan Dean deansusan@deanza.edu Barbara Illowsky Barbara Illowsky, Ph.D. illowskybarbara@deanza.edu Susan Dean Susan Dean deansusan@deanza.edu Barbara Illowsky Barbara Illowsky, Ph.D. illowskybarbara@deanza.edu Connexions Connexions cnx@cnx.org Maxfield Foundation Maxfield Foundation cnx@cnx.org diagram elementary probability statistics Venn Mathematics and Statistics This module introduces Venn diagrams as a method for solving some probability problems. This module is included in the Elementary Statistics textbook/collection as an optional lesson. en A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.Suppose an experiment has the outcomes 1, 2, 3, ... , 12 where each outcome has an equal chance of occurring. Let event A = {1, 2, 3, 4, 5, 6} and event A = {6, 7, 8, 9}. Then A AND B = {6} and A OR B = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The Venn diagram is as follows: Flip 2 fair coins. Let A = tails on the first coin. Let B = tails on the second coin. Then A = {TT, TH} and B = {TT, HT}. Therefore, A AND B = {TT}. A OR B = {TH, TT, HT}. The sample space when you flip two fair coins is S = {HH, HT, TH, TT}. The outcome HH is in neither A nor B. The Venn diagram is as follows: Forty percent of the students at a local college belong to a club and 50% work part time. Five percent of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let C = student belongs to a club and PT = student works part time. The probability that a students belongs to a club is P(C) = 0.40. The probability that a student works part time is P(PT) = 0.50. The probability that a student belongs to a club AND works part time is P(C AND PT) = 0.05. The probability that a student belongs to a club given that the student works part time is: P(C|PT)  =  P(C AND PT) P(PT)  =  0.05 0.50  =  0.1 The probability that a student belongs to a club OR works part time is: P(C OR PT) = P(C) + P(PT) - P(C AND PT) = 0.40 + 0.50 - 0.05 = 0.85 Venn Diagram The visual representation of a sample space and events in the form of circles or ovals showing their intersections.