Calling all mathematicians!

vanity

[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?

[mtbopfuyn]

Just a quick update. Woo hoo! Happy dance! Hurdled through the cuts and reached THE BIG TA-DAH! Thanks.

[Robert A Cook PE]

Almost everyone doing hurdles also entered the 500. However, few who do the 500 entered the hurdles.

Ah, but what success rate does a person have in a event? Just entering both doesn’t indicate a person will do well enough to place 1-2-3 or 4 in either.

(I had this happen in HS math competitions. Was “good enough” to do well and get trophies in the quick, 1/2 hour slide rule competitions at the “novice” level, but not good enough to get even top five routinely at the “veteran” level.

Cross-competed in a 3-hour science test, and did very well against the same people who were beating me in slide rule. I did well in long events, they did much, much better in “sprint” events.

So, don’t look at averages, look at “top performance” in the two events. The guy (or girl) who can get 1 or 2 place vice the guy who who “might make 3-4 is the better bet, since they aren’t allowing double entries.

[SouthTexas]

Good deal!