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Math paradox?

  1. Oct 19, 2009 #1
    can anyone answer this one?

    The baseball series has 4 teams in it and two are from los angeles. What are the chances of a Los Angeles team making it to the world series, at first I said simple. 50% but is this true? The dodgers are playing Philly, and in theory Philly has a 50% chance of making it to the series as does each individual team, but is there a weight measured for a los angeles team in general making it? Two teams are from LA and that cant equate to equal measure to the other indivdual teams. How would you measure this?
     
  2. jcsd
  3. Oct 19, 2009 #2

    Office_Shredder

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    Assuming that each team has a 50% chance of winning their series, the four possibilities are:

    LA vs LA - 25% chance
    LA vs NY - 25% chance
    Phi vs LA - 25% chance
    Phi vs NY - 25% chance

    So there's actually a 75% chance a team from LA makes the world series. If the probabilities of each team winning their respective series is different, you can use the fact that each series is independent to calculate the respective probabilities of the four outcomes
     
  4. Oct 20, 2009 #3
    I was having a debate with my dad about this. I actually told him shortly after that I realized it was actually 75%. He remains completely unconvinced, telling me to look up Boolean Algebra and ridiculous theories like 1+1=1. Probably through some esoteric proof he thinks that it's somehow 50%. Is he on track or completely wrong?
     
  5. Oct 20, 2009 #4

    D H

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    Your Dad is completely wrong. This is a simple probability problem. No paradox. It is in fact identical to determining the probability that at least one of the children in a family comprising two parents and two children is male (or female). Answer: 75%.

    However, in this particular case, the probability is currently a lot slimmer than 75% that at least one LA team will be in the World Series. The four possible matchups ( Yankees vs Phils, Yankees vs Dodgers, Angels vs Phils, and Angels vs Dodgers) were not equiprobable events prior to the start of the ALCLS and NLCS and are even further from equiprobable events now.
     
    Last edited: Oct 20, 2009
  6. Oct 20, 2009 #5

    uart

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    Sorry I don't know how the basball series works so I have to ask a really dumb question.

    Do two of those four teams make it to the world series or is it only one that makes it?
     
  7. Oct 20, 2009 #6

    uart

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    Ok I think I get it. Those four teams are all that's left and they'll play it out in a semifinal round to determine which two of them play each other for the WS. Is that correct?
     
  8. Oct 20, 2009 #7
    The world series would be pretty boring if there was only one team there :)

    Also, there is a 0% chance there's two teams from LA because the yankees are going.
     
  9. Oct 20, 2009 #8

    D H

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    uart, that is correct. The NY Yankees are playing the LA Angels for the American League Championship and the Philadelphia Phillies are playing the LA Dodgers for the National League Championship. The winners of these two championship series will play each other in the World Series.

    The Yankees are the heavy favorite to win the whole enchilada. They currently lead the Angels two games to one in the ALCS. First to four games wins the series. As both teams have two home games left (if needed), the Yankees are still heavily favored over the Angels in the ALCS. The Phillies were a slight favorite over the Dodgers prior to the onset of the NLCS. Now, with a three games to one lead over the Dodgers in the NLCS, the Phillies are extremely likely to take the NLCS.

    The Yankees facing the Phillies is the most likely outcome right now, much better than 50% if you are a gambling sort.
     
  10. Oct 20, 2009 #9
    You overlooked something...

    Let's call the Dodgers "LA1" and the Angels "LA2"
    The possible outcomes for who plays in the world series are then as follows:
    LA1 vs LA2 - 1/6 chance (approximately 16.7%)
    LA1 vs NY - 1/6 chance
    LA2 vs NY - 1/6 chance
    LA1 vs Phi - 1/6 chance
    LA2 vs Phi - 1/6 chance
    NY vs Phi - 1/6 chance

    The only situation in which an LA team doesn't make it to the world series is NY vs Phi. Therefore there is a 5 * 1/6 = 5/6 chance
    (83.33% approximately, more precisely [tex] 83 ^1/_3\%[/tex])
     
  11. Oct 20, 2009 #10

    nicksauce

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    No, it doesn't work like that. The world series must consists of one team from the American League (Yankees or Angels) and one team from the National League (Dodgers or Phillies)
     
  12. Oct 20, 2009 #11

    D H

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    No, you are overlooking something. "LA2 vs NY" and "LA1 vs Phi" are impossible World Series combinations.
     
  13. Oct 20, 2009 #12
    I stand corrected!

    75% it is! (Assuming equal probabilities between any of the 4 possible outcomes).
     
  14. Oct 20, 2009 #13

    uart

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    Ok thanks DH.

    BTW I had also worked out a 5/6 probability (all teams considered equal) but that was based on a random draw for the semi-finals which included the possibility of LA1 versus LA2 in the semi-final. Given the extra info about the restricted pairing possibilities then yes I also get the answer of 3/4. :)
     
  15. Oct 20, 2009 #14

    D H

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    I take it that neither you, uart, nor you, zgozvrm, is a sports fan.

    The exact details of which teams get to play in the World Series might be a bit arcane to a non-baseball fan. The concept of a ladder of eliminations is basic to almost all sports. The idea of a random draw to decide who gets to play for the big enchilada is anathema to any sport.
     
  16. Oct 20, 2009 #15

    uart

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    I'm from Australia and no baseball is not a particularly big sport here.
     
  17. Oct 20, 2009 #16
    Basketball fan, yes. Baseball fan, not so much.

    Basketball works similarly: East vs West in the Finals. Didn't know Baseball was that way too.
     
  18. Oct 20, 2009 #17

    D H

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    It doesn't matter. Australian football and cricket (especially cricket) are bizarre sports to Americans. However, I do know with absolute certainty one thing about cricket: The Cricket World Cup certainly does not have a series of eliminations that narrow the field down to six teams, out of which two are chosen at random to play in the final match.

    Think about it.
     
  19. Oct 20, 2009 #18
    You're misunderstanding the structure; it's probably very similar to your Cricket World Cup.

    There are 4 teams remaining (not 6). 2 of them are in the American League, and 2 are in the National League. The American League teams play each other until there is only one team left (the American League champs). The National League does the same, resulting in the National League champs. At the end, you will have one American League team playing one National League for the World Series.

    There is nothing random about who is picked to play in the World Series. Only in who wins.
     
  20. Oct 20, 2009 #19

    uart

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    Hey I knew that I didn't have enough information about the series to make the calculation that's why I asked for more info. Prior to getting that info however I worked with the assumption that all possible pairings were equally likely, that's all.
     
  21. Oct 20, 2009 #20
    Ok, so I received this email from my dad this morning, he is clearly wrong. But help me disprove the faulty logic.

    "here is a prove that your 25% reasoning is not working:

    Phil (NotLA) vs. Angels (LA) - 25%
    NY (NotLA) vs. Dodgers (LA) - 25%
    Dodgers (LA) vs. Angels (LA) - 25%
    Phil (NotLA) vs. NY (Not LA) - 25%

    LA presnt in 3 cases out of 4 which sugest 75% probability of LA to get into finals
    But wait NotLA is also presnt in 3 cases out of 4 which sugest 75% probability of NotLA to get into finals
    Both LA and NotLA have the same grater then 50% probabilty to get into finlas which is clearly wrong, so this logic can not be applied. 50% is the right answer"
     
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