Bluman A.G. Elementary Statistics- A Step By Step Approach

216 Chapter 4 Probability and Counting RulesTree diagrams can be used when the events are independent or dependent, and theycan also be used for sequences of three or more events.Objective 4Find the conditionalprobability of an event.Conditional ProbabilityThe conditional probability of an event B in relationship to an event A was defined as theprobability that event B occurs after event A has already occurred.The conditional probability of an event can be found by dividing both sides of theequation for multiplication rule 2 by P(A), as shown:PA and B PA • PBAPA and B PA • PB APA PAPA and BPA PBAFormula for Conditional ProbabilityThe probability that the second event B occurs given that the first event A has occurred can befound by dividing the probability that both events occurred by the probability that the firstevent has occurred. The formula isPA and BPBA PAExamples 4–32, 4–33, and 4–34 illustrate the use of this rule.Example 4–32Selecting Colored ChipsA box contains black chips and white chips. A person selects two chips without15replacement. If the probability of selecting a black chip and a white chip is 56, and the3probability of selecting a black chip on the first draw is 8, find the probability ofselecting the white chip on the second draw, given that the first chip selected was ablack chip.SolutionLetThenB selecting a black chipPWB PB and WPB5 1556 3 8 1556 • 8 3 1556W selecting a white chipHence, the probability of selecting a white chip on the second draw given that the first5chip selected was black is .7 15563871• 8 5 3 714–36