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Buying Solve this Mathematical Problem - $20 + Project

Discussion in 'Programming' started by Jake Howard, Oct 26, 2013.

  1. #1
    Hi All,

    I am looking for someone to solve a mathematical problem for me ($20) and an additional ($30) if they can convert it into a calculator in Excel.

    The first person to PM me the correct answer with workings on how they reached the answer will receive the $20. They will then receive an additional $30 if they can convert it (plus a few more variables) into an Excel File.

    Here goes:

    Usain Bolt is lining up to run in the 2016 Olympic Mens 100m final. He is the $2.00 favourite (in a 100% Market) to win the event, meaning that the probability of him winning the event is 50%.

    There are a total of 8 runners in the race, and Usain's seven opponents are all of lesser but equal ability and each have a 7.14% chance of winning ($14).

    Question:

    If Usain Bolt is a 50% chance of winning the race, what is the probability of him winning a medal (Gold, Silver or Bronze)?
    Jake Howard, Oct 26, 2013 IP
  2. Jake Howard

    Jake Howard Active Member

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    #2
    Hi All,

    I am currently in discussions with a DP Member who has provided me with workings for an answer of 87.5%

    Kind regards

    Jake
    Jake Howard, Oct 27, 2013 IP
  3. sachin410

    sachin410 Prominent Member

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    #3
    You can verify the answer.

    Add up all probabilities - Bolt at 1st place, Bolt at 2nd place...Bolt at 8th place. The answer should be 100%.
    sachin410, Oct 27, 2013 IP
  4. vishals

    vishals Active Member

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    #4
    This seems wrong. This solution sums up the three cases of Bolt winning 1st, 2nd, and 3rd. 1/2 * 1/2 * 1/2 = 1/8 is the odds that he loses all.

    But this is wrong cause it assumes that the odds of his winning silver and bronze are the same 1/2. Thats not true, cause his odds of winning silver are higher. His odds of winning bronze are higher still.

    Lets say there were only 4 guys running. With bolt's prob. of gold at 1/2, and rest three evenly divided at 1/6 each. What are the odds that Bold will win gold/silver/bronze? The odds that Bolt can win against the third person for bronze are not 1/2, but 1/2 divided by (1/2 + 1/6) = 3/4. His odds of winning silver are 1/2 divided by ( 1/2 + 1/6 + 1/6) = 3/5. The total odds of losing all of three medals are 1/2 * ( 1- 3/5 ) * ( 1 - 3/4) = 1/20.

    thats for 4 players. you calculate for 7 players.

    A good way to think about it is this: If there are just 3 players running, Bolt will definitely win all three medals.

    If there are infinite players running ( and bolts probability of winning gold is 1/2), then in case he loses the gold, then his odds of winning silver are also 1/2, because that are his odds of winning against infinite players. Same for bronze. In THAT case are Bolt's odds of winning either of the medal equal to ( 1 - 1/2 * 1/2 * 1/2) = 87.5 %.

    All the cases of players numbering 4, 7 or any other number, come in between these two cases.

    Hope I get some dollars, but if not thats cool!
    vishals, Oct 30, 2013 IP