Lottery Analysis

However, before the promotion could get final approval, questions arose over the process being fair and impartial.  Upper management were concern about sexism backlash from it being advertised as a “Guys Night Out” promotion, especially since the drawing for a trip to Hawaii was involved (in which 100% of respondents entered).  Therefore, Stan Goodman asked, if when someone is randomly selected from all respondents what is the probability that it is a woman.  The answer came back as 40.8% or 102/250.  Then Goodman inquired, “What is the probability that a woman who said yes would win the trip to Hawaii?”  In technical term this would be written as P(Y|W), which equals to 63/102= 0.6176 or roughly 62%.

After considering Goodman’s concerns, Maedup decided to dig deeper into the data that was presented and decided to add the age groups into the equation.  Maedup pointed out that since sales from women under 40 has been down, it would be optimal if the person randomly selected from the pool was a woman that said yes who is under 40.  The probability of a female who is under 40 and that responded yes to the promotion P(F|U∩Y) is calculated by dividing the number of female respondents that are under 40 that said yes (20/250). Maedup was not too happy to find out that the probability of that happening was only 8%.  At this point Maedup considered just adding the respondents that answered yes into the Hawaii drawing as that would be the audience that they would be targeting the most.  So he wanted to know what is the probability that a woman who is under 40 is randomly selected given that she has said yes to the promotion P(FU|Y) or 20/154 which still only equaled approximately 13%.  Next Maedup asked what are the chances of either female under 40 or someone that responded yes to the promotion would be randomly chosen.   This can be calculated by added the probability of a woman under 40 being chosen (43/250) and the probability of someone that responded yes being chosen (159/250) minus the probability of a woman under 40 who said ye being chosen (20/250) which would equal a 72.8% chance (0.172+.636-.08)