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OLd STEP question. Am I correct?

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Reply 20
Avatar for BabyMaths
BabyMaths
Original post by brianeverit
I now have what I believe is a definitive solution and has been confimed by Peter Mitchell who runs the Meiklerigg site


I'll post mine too.

STEP I 1991 q 16.pdf

I fully accept that I might be wrong but there it is, my best effort.
Reply 21
Avatar for brianeverit
brianeverit
OP
9
Original post by BabyMaths
I'll post mine too.

STEP I 1991 q 16.pdf

I fully accept that I might be wrong but there it is, my best effort.



If the Frog crosses at n=0 then the toad must cross at n>0 not just n=1, and similarly for all the other possibilities and I don't think you want that last term in the final denominator because that is the probability that the frog crosses safely during the third minute, i.e. AFTER 2 minutes.
(edited 10 years ago)
Reply 22
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BabyMaths
Original post by brianeverit
If the Frog crosses at n=0 then the toad must cross at n>0 not just n=1, and similarly for all the other possibilities and I don't think you want that last term in the final denominator because that is the probability that the frog crosses safely during the third minute, i.e. AFTER 2 minutes.


I see what you mean. I took the attempts to cross to be at n=0, n=1 and n=2 and the time required to cross to be zero. We're not dealing with reality here after all. :wink:
Reply 23
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brianeverit
OP
9
Original post by ghostwalker
What is the basis for Peter Mitchell being able to confirm it? Did he set the STEP question?


Peter Mitchell is a former Head of Mathematics at Newcastle Royal Grammar School. Chairman of the M.E.I. project, an Assos lecturer with the Open University and runs the Meiklerigg web site. Pretty good credentials I think.
Original post by brianeverit
Peter Mitchell is a former Head of Mathematics at Newcastle Royal Grammar School. Chairman of the M.E.I. project, an Assos lecturer with the Open University and runs the Meiklerigg web site. Pretty good credentials I think.
Whatever the qualifications, I don't agree with the interpretation here - to my mind "later on" strongly implies the road safety conditions for the two animals are to be taken as independent.

[As far as qualifications go, everyone makes mistakes. I corrected the head examiner for the maths tripos during my undergrad years. (Of course, he corrected me a heck of a lot more often!)].
Original post by brianeverit
...


As DFranklin so eloquently put it.

I stand by BabyMaths' answers.
(edited 10 years ago)
Reply 26
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brianeverit
OP
9
Original post by ghostwalker
As DFranklin so eloquently put it.

I stand by BabyMaths' answers.


I do now agree with Babymaths answer of 0.323 for the second part but still think the last answer is incorrect as he has considered the frog not arriving after 2 minutes. I get 0.78286 for this part.
(edited 10 years ago)
Original post by brianeverit
but still think the last answer is incorrect as he has considered the frog not arriving after 2 minutes. I get 0.78286 for this part.


I take P(not arrived after 2 minutes) to be not arrived at t=0, 1, or 2. As BabyMaths said, this is not a realistic situation. Since we're told the time to cross is negligible, I take that to mean we include the 2 minute time.

If the question had said 2 1/2 minutes or 1 1/2 minutes then there would be no ambiguity.

As it stands I take the "negligible" as an attempt to remove the ambiguity, but it is still there really.

I go with BabyMaths result, but I think it's arguable that your result is correct as well.
(edited 10 years ago)
Reply 28
Avatar for BabyMaths
BabyMaths
Original post by ghostwalker
I take P(not arrived after 2 minutes) to be not arrived at t=0, 1, or 2. As BabyMaths said, this is not a realistic situation. Since we're told the time to cross is negligible, I take that to mean we include the 2 minute time.

If the question had said 2 1/2 minutes or 1 1/2 minutes then there would be no ambiguity.

As it stands I take the "negligible" as an attempt to remove the ambiguity, but it is still there really.

I go with BabyMaths result, but I think it's arguable that your result is correct as well.


That pretty much sums up how I feel about the question.

If it had been written more carefully it would have been an OK question

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