Math Is Fun Forum

About the email I have just sent:
Just out of interest: I sent that at 12:57 - when did you get the email?

I have thought of another conversion you might like to do:

ounces to grams and grams to ounces

eg. 1 ounce = 28.3495 grams (perhaps round to 28g)
(use exact figure if more accuracy is needed then round at the end)

So for instance how many grams in 6 ounces ?
How many ounces is 100 grams ?

Be careful to make sure you have got that right if needed for a cooking
recipe and/or something important.

I don't think the weather has had any effect on the system (overheating etc.).
The thing that I thought was the weather turned out to be caused
by roadworkers making an error causing a connection failure.
I received the 2 emails where you asked for the questions only too
late and had just sent the answers and questions emails.
After a pause of 5 minutes or so I sent the questions only.
It may still help you to try to do those since you have the answers now
in case you are stuck with them. Notice also that I have answered two
of the recent maths exercises as examples in case you were stuck on them
(see above).

I am also going to do this one:

5 metres = 500 cm
To convert to inches I need to divide by 2.54

500 / 2.54 = 196.85 inches (to 2 dp.)

or 197 to the nearest inch.

I agree with bobbym in that it is the second line where the problem starts.

The square root function can only be used in this way if a disabiguation is made where
we either take the positive value so reverse a square of a positive number, or I suppose
take the negative value provided the original number was negative before being squared.
If there is no guarantee of the sign then both negative and positive cases of the number
squared then square rooted should be checked to see whether the equation is still true
in every case. Otherwise a true statement can imply an untrue one as you did purposefully. 

However in the quadratic formula for instance the square root sign is used to indicate
that you can take both the positive and negative square root so the square root has to
allow you to take either the positive or negative case.

So let us start with a negative number so -1 then square it and get 1 then square root it
and we get 1. That is the trouble with using a function like square root as an inverse.
It is good for calculating things, but in a formal proof I find it difficult, because care has
to be taken for instance not to accidentally make a sign error which I have sometimes
done by accident in a tutor marked assignment (I remember I accidentally fudged the sign
of an otherwise correct proof and had a couple of marks taken off. I think that I had done
the proof first with one sign error which I knew must be there somewhere. I searched for
the "error" and "corrected it" only to find that according to the tutor it had 2 sign errors
which cancelled).

Anyway your example gives a good case something of the kind happening with a very
amusing consequence.

(0.10*0.11 + 0.9*0.89)

To my mind this reads as P(flag | not spam) x P(flag) + P(~flag) x p(~flag | not spam)
Which using Bayes simplifies to: P (flag and not spam) + P (~flag and not spam)
Which perhaps also simplifies to: P (not spam)

0.10*0.11 / (0.10*0.11 + 0.9*0.89)

This I thought came from: P(flag and not spam) / P(not spam)

Is that what you meant and why you made that calculation?

If you let A = flag
and let B = not spam
Then apply Bayes of P (A and B) = P (A | B ) x P (B)
then this supports this logic.
But P(A | B) = P (flag | not spam)
unless I am mistaken we want P (not spam | flag)
So we want P (B | A) perhaps ?

P (B | A) x P(A) = P(B and A)

The trouble with that argument is that it does not work. Perhaps your answer is correct.

because P(B and A) = P (A and B)
so P (B | A) = P(A and B) / P(A)

The problem with that is that it gives us simply the answer 0.11 which does not make sense.
It would be daft to ask that question so are you sure you have formulated everything correctly
and consistently.
Make sure you use the term "flag" consistently and do not confuse with "spam".
Is 0.1 definately the probability that a random message is spam?
Not 0.1 being the probability that a random message is flag?

   given that 1/10 of message is a spam message.

   Does this mean that 0.1 of all messages are flagged as spam ?
   Or that 0.1 of all messages are spam ?

   So P(flag) = 0.1
   Or is it P(spam) = 0.1 ? (I think this version is more likely, but you have used the other)

I will have to stop for now. I am sharing your confusion about this it is a complicated problem
and the formulation of the probabilities originally is not very clear.

The detector has just detect a message as being spam. what is the probability that the message is actually not a spam message?

So we are looking for: P(not spam given that the message is flagged as spam)
Or using your notation: P(~spam | flag)

I am a little confused myself and I may need to think some more about this.....

I am not sure either way at the moment I am trying to draw a tree diagram on paper to help ....

Another question about feet, inches, cm and metres is:

A person is said to be 5 foot 9 inches tall exactly.

(1) How many inches is the person is just using inches ? (Hint: 12 inches equals one foot.)

(2) Now convert this into centimetres. (Remember: 1 inch = 2.54 cm)

(3) Now convert this into metres.

(4) You could also put this in the form of metres and centimetres.
(I mean by that to put 100cm as 1 metre and give the rest as centimetres.)

One thing you might like to consider is:

An object is said to weight one stone exactly.

1 stone = 14 pounds
1 kg = 2.20462 pounds

How much is one stone in kg ?

By kg or Kg or KG I mean kilograms that is to say 1000 grams.
"kilo" usually means 1000 of something.

No 100 / 2.54 = 39.37 inches approx.

Notice that 39.37.. x 2.54 = 100 cm

You can if you like divide by 12 to get the amount of feet in one metre.

All correct well done (except Q3). Try the one above if you haven't already.
Actually Q3 was 5000 /100 = 50 m
Anyway you have got the hang of it. Good.
I will go away for a few minutes for you to try the feet/inches/cm one.

I have been sent 3 emails to the BT address. Two were about 5:11pm one was about 9.43am.
I have replied to one of them. The two at about 5:11pm were "Blackberry" ones.
The one at about 9.43am was a mobile one.
Do you want me to give you the answer with a brief method for one or two of the recent questions?
Another idea I have had is for me to meet you online to ask just one question at a time for you
to try and me to give "correct" or "wrong" and say why if it is wrong and what it should be?
This has worked well before with some maths problems that you were stuck on.