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

Section 4–3 The Multiplication Rules and Conditional Probability 217Example 4–33Parking TicketsThe probability that Sam parks in a no-parking zone and gets a parking ticket is 0.06,and the probability that Sam cannot find a legal parking space and has to park in the noparkingzone is 0.20. On Tuesday, Sam arrives at school and has to park in a no-parkingzone. Find the probability that he will get a parking ticket.SolutionLetThenN parking in a no-parking zonePN and T PTN PN 0.060.20 0.30T getting a ticketHence, Sam has a 0.30 probability of getting a parking ticket, given that he parked in ano-parking zone.The conditional probability of events occurring can also be computed when the dataare given in table form, as shown in Example 4–34.Example 4–34Survey on Women in the MilitaryA recent survey asked 100 people if they thought women in the armed forces should bepermitted to participate in combat. The results of the survey are shown.Gender Yes No TotalMale 32 18 50Female 8 42 50Total 40 60 100Find these probabilities.a. The respondent answered yes, given that the respondent was a female.b. The respondent was a male, given that the respondent answered no.SolutionLetM respondent was a maleF respondent was a femalea. The problem is to find P(YF). The rule statesPYF PF and Y PFY respondent answered yesN respondent answered noThe probability P(F and Y) is the number of females who responded yes, dividedby the total number of respondents:PF and Y 81004–37