A general record of my ongoing battle with all forms of nonsense.

Tuesday, 1 December 2009

A quick maths quiz

Here's a quick maths quiz. Post your answers, ideally with your working and I'll be able to see how well they compare to mine.
  1. What is the probability of there being a single molecule of active ingredient in a 30C homeopathic remedy? Assume no contamination and pure water.
  2. What is the probability of winning the National Lottery 5 weeks in a row. You get one ticket per week of course.
  3. Which is more likely?
  4. How much would it cost to buy enough pills that you'd expect to have one molecule of active ingredient? Note: At Boots, they're about £5 for 84 pillules.
I'll post my answers tomorrow.

7 comments:

Paul N said...

1) a 30C dilution means that one portion of the active ingredient is diluted 100 fold (i.e. 10^2), 30 times. So each time you dilute it,by a hundred fold, add another two zeroes on to the end of the dilution factor,ending up with a dilution of 1 part of the original in every 10^60.

2) the probability of wining the UK National Lottery is 1 in 13,983,816, so the chance of winning the lottery 5 times in a row is the above fraction to the power of 5, in other words (1/13983816)^5, or 1.8701287 × 10^-36

You are more likely to win the lottery 5 times in a row than find a molecule of the active ingredient.

3) Assume 2 * 10^22 molecules of water in a drop (see http://wiki.answers.com/Q/How_many_water_molecules_are_in_one_drop_of_water)

Assume a pill contains one drop of active ingredient.

So, if you have a 30C dilution, you'll need 10^60 moleclues of water to get one molecule of ingredient,but a pill only contains 2 * 10^22. So actually, you'll need 10^60/(2*10^22) pills to get one molecule, i.e. 5.0 × 10^37 pills.

At 4.99/84 a pill (around 5p a pill), it will cost you 5 * 10^37 * 4.99 /84 = £2.9702381 × 10^36

or approx 3 trillion trillion trillion pounds.

Zeno said...

See Zeno's answers.

Some slightly different assumptions to Paul, but very similar answers.

Zeno said...

Sorry, the link should be:

Zeno's answers.

DavidP said...

I disagree with Paul and Zeno's answers to the first question. 1 molecule in 10^60 is from the original solution, but by Zeno's calculation, there are 1/1273 mol of molecules ( = 6.02*10^23/1273 molecules)in the final drop, so the chance of there being a single molecule from the original solution is 1 in 10^60/ (6.02*10^23/1273) i.e. 1 in 2*10^39. Zeno gives this as "2.11E+39 pills for 1 molecule of substance" so his calculation is correct, he just selected the wrong number as his answer for question 1.

BUT the original solution often has very little 'active ingredient' - it's often extract, sometimes of an insoluble substance, so the answer to Simon's question varies from 1 in 2*10^39 to perhaps 1 in 10^48 (mother extract being 1 part per billion), with a typical value of probably 1 in 10^41 (1-2% solution)
So Simon has chosen his question carefully - you are more liklely to win the lottery 5 times in a row (starting with the next time you enter) than you are to have a single molecule of the active ingredient in a 30C pill, but may be less likely to win it 6 times in a row, depending on the mother tincture.

Of course in the U.S. they destroyed people's sense of smell with a 1X 'homeopathic' cold remedy that was around 33 millimolar zinc gluconate cited here which I make to be about 0.2% zinc by weight.

Simon said...

Answers to the quiz are up on my blog

Dr, said...

Homeopathy cures even when Conventional Allopathic Medicine (CAM) fails

Zeno said...

Hi Dr Nancy Malik! Fancy seeing you here.

Still not want to stand by your promise of proving you can tell the difference between water and one of your magic homeopathic potions? No? Didn't think so.