The following question appeared in \"Ask Marilyn\" in Parade Magazine on October
ID: 3217155 • Letter: T
Question
The following question appeared in "Ask Marilyn" in Parade Magazine on October 10, 2004. At we gave away some stereo speakers by drawing names, only employees who wanted to win included three of my friends I didn't want the speakers, so I didn't join them. Would t have helped their Chance if I'd signed up and If i won, held a second drawing just for them?... Ken Glade, Goshen NY To find the answer to Ken's question, we first need to create a scenario to work with. Let's assume that there are 12 total people in the office: Ken, Ken's three friends, and other people of Ken's three friends, one of them will be named Ann. Scenario Ar Let's assume first that Ken does not enter the drawing, but everyone else in the office does. Therefore, there are 11 people in the drawing, where one the people is Ann. What is the probability that Ann wins the drawing? scenario B Now let's assume that Ken does enter the Therefore, al 12 people will participate If Ken wins the initial drawing he will hold a second drawing that only his three friends (including Ann) will entre. What is the probability that Ann take home the speakers? Comparing the results of Scenarios A and B you will find that Ann has a better chance of winning the speakers If Ken enters the initial drawing and then holds a second drawing for his friends.Explanation / Answer
In Scenario A, Ann is one amongst the 11 people. (Since Ken is not participating)
Therefore the probability of her winning is 1/11 = 0.091
In Scenario B, There are 2 parts.
First, Ann wins amongst the 12 people(including Ken) = 1/12 or
Ken Wins amongst the 12, and then in the redraw of his 3 friends, Ann wins
= 1/12(for Ken winning) * 1/3 (for Ann winning amongst the 3)
= 1/12*1/3 = 1/36
Therefore the Probability that Ann takes home the speaker = 1/12+1/36 = 1/9 = 0.11
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