Answers to jury questions must be responsive and must not deter further questions: R v Layton  SCC 36 (23 July 2009).
If the jury has a copy of the judge's summing up then mere repetition of the words used in it is not likely to be responsive. Here, a direction on the standard of proof led to a question seeking clarification. A difficulty arose because the law is reluctant to elaborate on what "beyond reasonable doubt" means, apart from the standard direction.
It is easy to see why the phrase "beyond reasonable doubt" causes trouble to jurors. It is a description of the required level of proof, which may be thought of as going in one direction, yet at the same time it is expressed in terms of doubt, which tends in the other direction.
As lawyers we are so used to the expression "beyond reasonable doubt" that we take its meaning for granted, ignoring this contradiction in the composite concepts. Even though juries frequently ask for further assistance on the meaning of "beyond reasonable doubt" (see also R v Griffin  SCC 28 noted here 19 June 2009), the law is not clear on what more should be said.
In Layton the standard R v Lifchus, 1997 CanLII 319 (S.C.C.),  3 S.C.R. 320 direction had been given. In the second day of its deliberation the jury returned with this question:
"Jury requests clarification on reasonable doubt section of charge to the Jury. Particularly difference between absolute certainty and balance of probabilities"
citing the relevant part of the standard direction.
In the terms I mentioned above, although the first sentence refers to doubt, the second is about proof.
The standard direction contained this phrase: "...the reasonable doubt standard falls much closer to absolute certainty than to proof on a balance of probabilities."
Given that the jury had this in writing, why the question?
It's a mystery to lawyers, and it is not surprising that counsel in this trial had been unable to offer much by way of assistance to the judge in her preparation of the answer.
Perhaps the jury was really seeking clarification on doubt: how much difference is there between no doubt (absolute certainty) and the balance of probabilities? That is a sensible question, because proof on the balance of probabilities can be achieved by elimination of any of a range of doubts. To put it mathematically (as the law doesn't but as people do tend to: see note on R v Wanhalla 25 August 2006), proof on the balance of probabilities may leave no doubt, or up to 49% of doubt. It would be over-proof, but the result would be the same for leaving any level of doubt in that range. For example, if a doubt of 25% remained, it would still be correct to say that the plaintiff had proved his case on the balance of probabilities. So too if the doubt was 10% or 49%. But if the doubt was 51% or more the plaintiff would have failed to prove his case on the balance of probabilities.
The most helpful way of answering the question would be to say that the balance of probabilities is satisfied even though there may be 49% doubt, and absolute certainty is where there is zero doubt. The criminal standard of proof tolerates much less doubt than the balance of probabilities: much closer to zero doubt than to 49% doubt.
But the law doesn't approve of the use of approximate figures or mathematical analogies. The two cultures persist.