Posted on 12/31/2007 5:33:59 AM PST by mtbopfuyn
I’m sure this is elementary but I need some help with a probability. Two trains leave the station…. nooo, scratch that. Let’s say there are two Track and Field competitions, one is the 500 meter and the other is hurdles. Neither competition is harder than the other, just slightly different.
500 meter competition – The top 4 places from local competition advance to the preliminary competition and meet with 3 other groups of top 4 placers. Those 16 compete and the top 2 make THE BIG TA-DAH!
Hurdles competition – Only the 1st place person from the local competition advances to the preliminary competition to meet with 3 other persons who made 1st at their locals. Those 4 compete and the 1st place person advances to the next round (the 500 doesn’t have this round). That person then competes with 6 others (total of 7) and the top 3 make THE BIG TA-DAH!
Now, throw in these variables –
1) Almost everyone doing hurdles also entered the 500. However, few who do the 500 entered the hurdles.
2) If a person qualifies locally in the 500 as well as the hurdles, he is not allowed to compete in both. He must choose one event.
3) When a person who qualifies for both chooses their one event, an alternate is moved up into the competitions. For example, if a 4th place meter runner chooses his 1st place hurdles then the 5th place runner, the alternate, is moved up to 4th place.
4) We do not know the other competitors' times nor have any idea how well they did in previous competitions. We also do not know if a there are alternates in the standings.
FIND THE PROBABILITY -
1) Which event should the person choose to have better odds at making THE BIG TA-DA?
2) Which ranking (1st, 2nd, 3rd, 4th) in the 500 would be the deciding point to have better odds in choosing the 500 over the hurdles?
what is chasing you?
levels of inspiration to run can be a big factor
You do have a point. Naw, just chasing after THE BIG TA-DAH but don’t have a pig’s chance. But I did up grade with new pair of super-duper shiny new running shoes, so there’s always hope.
Make friends with the scorekeeper. Even if he’s French.
The hurdling event. Chicks dig hurdlers; giving you a much better shot at THE BIG TA-DA.
Point one: Choose the 500. You have 2/16 (12.5%) chance of achieving the BIG-TA-DAH competing with a field 12 of whom are already known to have done worse than you in at least one contest. In the hurdles, you have a 3/28 (10.7%) chance in a field where the 27 others may all be as good as you are.
Point two: For most people the question is irrelevant, assuming the starting fields for the prelim contests in both sports are the same size, as only the top 25% of the 500 qualifiers even have the choice to make. If a given individual does, however, it reinforces the earlier advice, because it means he’s in the top 25% of 500 advancers, but says nothing about his chances in the hurdles.
Oh, come on FRiends. This is quickly moving off the front page and not a solution yet.
FYI, I chose the hurdles without much heads up on the number of rounds or the odds. I’m not sure I chose correctly or if it was wise going into debt by investing in such expensive new shoes. The old shoes might have been ok in the 500 but they wouldn’t have made it off the starting block in the hurdles. I’ll know Saturday one way or the other.
I was vaguely told my standings in the local 500 were 2nd or 3rd place. That placed me somewhere in the middle of the pack. The hurdles competition is unknown and that pesky extra round is muddying up the field by making the final 7 competition even stiffer. So, it's either take a chance at the unknown hurdles or go in knowing others are faster than you in the 500.
Yeah, I had a moment of mental flatulence and calculated as if those who could choose either would have to have finished first in the 500’s as well as the hurdles. Nevertheless, the advice stands. 2 in 16 is better than 3 in 28. Ignore the two stage nature of the hurdles championships. It’s exactly the same as one more round in a playoff that starts with 28 entrants. For example, in the 500 championships, with 16 initial entrants, you will have to win 3 rounds to get to the final two, with each round probably getting more challenging as the cream rises to the top. Same story as the hurdles, except 12.5% of the starters get the brass ring, as opposed to 10.7% of the hurdlers.
Will you tell us what the heck we're talking about on Saturday? Is it some sort of job/promotion thing?
Not that it’s any help in finding the solution to the problem, but choosing hurdles opened a slot for my right hand man to move up to one place outside of the over all 500 standings. Though not high enough for advancement, but if one person up the line drops out we get another team mate in for the big pat on the back.
Yeah, the basic odds are slightly better with the 500. It was the fact that I didn’t know exactly where I stood in the 500 pack and not knowing about the extra hurdle round. If I were 1st or 2nd in the 500 then there’d be no question however, if I were 3rd then... that’s where things got dicey. That’s why I threw caution to the wind and went with the 1st in hurdles.
Yeah, if you’re near the middle of the pack of runners and the overall odds in both sports are close, the best advice is probably to go with the sport you like better / feel more confident in.
Yes, it’s a chance at working with the elite. And of course the glory, if I make it, will most definitely lead to better offers.
Go for the 500 meter.
Better odds and .... no hurdles!
Seriously, each hurdle is a variable beyond speed and time.
Timing, pace, and form each contribute to the probability of failure.
For instance:
CASE I: It assumed that the outcome is causal, that any individual has fixed and completely repeatable, but unknown a priori ranking against all individual.Even with this smoothed d out you may only have a parmetric solution. BTW, where did the other six competitors come from for the second round of third round of the hurdles competition?CASE II: Alternately the outcome of any round (heat) completely random, any individual has the same chance of achieving any particular outcome on a given trial as any other.
CASE III: Each individual has a different and distinct skill level, put the operation of chance will produce somewhat different outcomes in any one trial.
“Which event should the person choose to have better odds at making THE BIG TA-DA?”
Will you tell him or shall I, how to get to this big TA-DA???
(innocent look)
(smirk)
The other competitors come from their perspective local competitions and move up as in any elimination chart.
In the hurdles, you should also consider the impediments AND those of the runners on each side of you. While it's possible for runners to get out of their lanes and cause you problems, it's far more likely in the hurdles.
Good luck!
How about you do your own homework assignments?
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