If you are mentally ill, what is the probability that you are a murderer?

With regard to the proposed mental health bill going through the UK parliament today:

I find it interesting that according to the Department of Health ministerial statement: 1 in 6 people suffer from a mental illness in a given year.

According to another Department of Health statement 50 homicides a year are committed by the mentally ill. Given there are roughly 800 homicides a year in the UK that means 1 in 16 homicidal people are mentally ill.

Less than the going rate in the population. So, rational people are more likely to kill than the mad.

But any little helps eh? and if you are one of the 14,000 people a year who will have their liberty constrained under the bill (A BBC figure, no idea as to the source) at least we can be 99.6% sure that you are not about to kill someone.

(No doubt there are definitional problems that mean all these statistics are incorrect).