Probability Question

M

Monkeyseat

Full Member
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Jul 3, 2005
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Hello.:)

[Question]
"Katie is running in a 100 metre race. There are six runners.
Explain why the probability that Katie will win is NOT 1/6".

[Difficulty]
All of it.

[Thoughts]
If her probability of winning is not 1/6, then it is because of some
information about the relative abilities of the runners. Since we
aren't given any such information, it is not possible to determine
the probability for Katie (or any of the others) to win.



Sorry I'm just a bit confused because it's not really answered the question, it's just suggesting why...

Any help? Thanks!:)
 
Hi Monkeyseat,

I think you have a good explanation there. The probability of Katie winning would be 1/6 if and only if all six runners were, in every way, equally skilled runners. But since, like you said, we don't know what Katie's skills are relative to the others, we can't know if they are equally skilled, and therefore cannot say that her chances of winning are 1/6.

Minor point: The problem seems to say that the probability of 1/6 cannot happen. But it can: it definitely is possible that she wins with a probability of 1/6 (because it's definitely possible that all six runners are equally skilled). We just cannot say for sure that it is 1/6 (because we don't know for sure that the runners are equally skilled).

I hope this makes sense!
 
Hello, Monkeyseat!

I agree with you and Matt . . . and here are my thoughts.

Maybe they want us to compare this situation with a more "random" one.

Selecting one number at random from a bowl containing six numbers,
. . the probability of any particular number being chosen is 1/6.

With a race involving six people, the winner is not randomly chosen.
The winner is decided by who is the fastest. . (That's what a race is for!)

People who are knowledgeable about the past performaces of the six runners
. . (say, coaches and deficated fans) will have more information.
But it is certainly not a random choice . . . ask any bookie.
 
May all students learn presentation from Monkeyseat. Very nice and very helpful.
 
Matt said:
Hi Monkeyseat,

I think you have a good explanation there. The probability of Katie winning would be 1/6 if and only if all six runners were, in every way, equally skilled runners. But since, like you said, we don't know what Katie's skills are relative to the others, we can't know if they are equally skilled, and therefore cannot say that her chances of winning are 1/6.

Minor point: The problem seems to say that the probability of 1/6 cannot happen. But it can: it definitely is possible that she wins with a probability of 1/6 (because it's definitely possible that all six runners are equally skilled). We just cannot say for sure that it is 1/6 (because we don't know for sure that the runners are equally skilled).

I hope this makes sense!
Click to expand...

Yeah that's what I thought.

The book I am working from is really old and half the questions are stupid.

Here's a picture of the actual question:

http://img271.imageshack.us/img271/9963/hpim08158ln.jpg

But I thought if her probability was 1/6 it is not necessarily even chance each as some could have a probability of a 1/12 couldn't they?

Thank you to all those who replied! :)
 
The spinner data (which didn't come thru on my computer) changes the question. I assume the directions give the information that soroban wanted from the coaches and fans. It probably gives areas for each of the six runners with the probability that that runner will win being the area. The probabilities will add up to 1 (the area of the spinner circle.) If you need more, copy the shading info here (or maybe others got to see the whole question and will do more,)
 
Matt: "The probability of Katie winning would be 1/6 if and only if all
six runners were, in every way, equally skilled runners"

Disagree...then, all 6 runners will always tie :)
 
Denis said:
Matt: "The probability of Katie winning would be 1/6 if and only if all
six runners were, in every way, equally skilled runners"
Disagree...then, all 6 runners will always tie :)
Click to expand...
But in that case, we would have to roll a die to determine the winner. Someone has to receive the one gold trophy that was made for the race. :wink:
 
So, my answer is correct? Anything else I could add?

And the probability of all the runners doesn't have to be a 1/6 each does it?

Thanks. :D
 
Please reread my reply and look at the shading directions for the spinner in your book. That will tell you what the odds (for each runner?) are. From the question, no area (or if it tells you which runner Katie is, her's) should be 1/6th of the circle.
--------------------
Gene
 
Gene said:
Please reread my reply and look at the shading directions for the spinner in your book. That will tell you what the odds (for each runner?) are. From the question, no area (or if it tells you which runner Katie is, her's) should be 1/6th of the circle.
--------------------
Gene
Click to expand...

The spinner shading is a completely different question...

That's why I didn't take a photo of it.. :wink:
 
Whoops, you are right. I misread it. :oops: It made so much more sense (to me) that there was something, somewhere that gave the odds that I leaped to a bad conclusion.
--------------------
Gene
 
I can't improve on your first thoughts. I, for one, would be very interested in the books answer. I have to disagree with those who say they must be evenly matched. Consider a team with four who couldn't win even if Kate and Fred each broke a leg. Fred however beats Kate 5 times out of 6. Kate wins 1/6th of the time.
With the info presented I don't see any way of showing that her probability is or isn't 1/6.
I will be patiently waiting for an explaination of the book's reasoning. 1/6 seems, to me, to be the "best" answer.
--------------------
Gene
 
Gene said:
I can't improve on your first thoughts. I, for one, would be very interested in the books answer. I have to disagree with those who say they must be evenly matched. Consider a team with four who couldn't win even if Kate and Fred each broke a leg. Fred however beats Kate 5 times out of 6. Kate wins 1/6th of the time.
With the info presented I don't see any way of showing that her probability is or isn't 1/6.
I will be patiently waiting for an explaination of the book's reasoning. 1/6 seems, to me, to be the "best" answer.
--------------------
Gene
Click to expand...

I wish I could have an answer too, but there's no answer book... :roll:

Thank you to everyone who has helped. :D
 
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