A Very Hard Easy Probability Question

Here is a question I set my students today. It is, mathematically speaking, very easy. It can be solved using mental arithmetic, and requires no complicated formulae or advanced concepts at all. It is not a trick question. However, people always find it incredibly difficult to get right, and many people fail to understand the solution once it has been explained to them. I have had vitriolic arguments with distinguished colleagues who refuse to accept my reasoning. What do you think? I will post my answer in a day or two, but in the meantime let's hear some suggestions...

The question is this. Imagine you have been tested in a large-scale screening programme for a disease known to affect one person in a hundred. The test is 90% accurate, and you test positive. What is the probability that you have the disease?

Understanding this kind of question is very important, because it leads to exactly the dilemma you might face if you were screened for a major killer like breast cancer or testicular cancer, and tested positive. Should you immediately opt for a risky procedure to investigate further, or would that be to submit yourself to unnecessary surgery? Gerd Gigerenzer wrote the book Reckoning With Risk about this kind of problem (it's a brilliant book too, so read it if you can), concluding that thousands of people are facing unnecessary dangers because of poor understanding of probability. Over to you...

Happy New Year!

New academic year, that is. By 'eck, it's been a busy, wet summer. I really feel like I need a holiday, but instead here come hundreds of new students. Welcome to Preston, guys! Here's a few bits and pieces to start with...

I'm doing 10:10. Are you? Follow the link, and pledge to reduce your carbon footprint by 10% in 2010. Also, while I am in campaigning mode, watch THIS FILM too. Good, isn't it?

Now, if that was a bit serious for you, check out this beautiful model pig. I love the customer reviews underneath! If it was just a bit cheaper I would definitely buy one.

What else is new in the world of quack (or should that be "oink") medicine? Following a campaign by Sense About Science, the WHO declared that homeopathy should NOT be used to treat HIV, TB, malaria, influenza or infant diarrhoea. Wahey! This is perfectly sensible advice, of course, since homeopathy is completely useless for all these conditions (as it is for all conditions, in fact), but it is still nice to see the WHO taking a stand. The reaction of the homeopaths has been predictable: the usual bluster, whining and cherry-picking of evidence. When will we be rid of these murderous imbeciles? Homeopathy is dead, dead, dead, but the corpse just keeps on twitching.

Meanwhile, Simon Singh's libel case against the back-crack quacks rumbles on, but legal blogger Jack of Kent has decided to take a sabbatical from blogging! How will I keep up now? I hope this does not mean I have to swallow my pride and join the infernal tweety thing.

I have been ill myself for the past couple of weeks, but there is one complementary medicine I do approve of and sure enough, a few doses of uisge beatha have made me feel a lot better (I like to use it in conjunction with a few crystals of dihydrogen monoxide, to enhance the effect). My trip to the Rebellion festival was probably the cause of my malady: I am really too old now for a four-day bender of alcohol, junk food, late nights and serious mayhem. Not that it will stop me going again next year! Here are a couple of highlights - the Exploited and the UK Subs. See what you missed?