Trout

iTrader: (1)

I came across this as a simple test of the ability of bankers to assess risk - indeed not just bankers, any typical human!


There is a fatal disease that kills 1 in 1000

A test has been developed that is 95% accurate.

Your doctor tells you that your test is positive.

What are your chances of surviving?

stilover

100%

I'm there to pick up a friends test results.

tony de wonderful

The first sentence is ambiguously worded.

1 in 1000 of what? Infected people? Total population?

scoobyster

Nice. 98% I think?

PaulC72

Best start living like I am infected just in case, if it goes to court I can plead temporary insanity due to the stresses of the potential infection..If I die it'll be happy.

DCI Gene Hunt

Slim to none

hodgy0_2

5%

stevie boy

999 in 1000

hodgy0_2

irrelevant -- much like you

Trout

iTrader: (1)

Of the population.

Someone has got it right and someone has got it wrong.

I got it wrong and had to think hard about it! The natural inclination is to get it wrong.

Dunk

iTrader: (1)

Great question, really makes you think, my money's on.....98%

D

AndyC_772

iTrader: (2)

If the disease kills everyone who catches it, and you're told you have a 95% chance of having it, then there's a 95% chance you'll die. The prevalence of the disease across the general population doesn't matter. But that's NOT what a "95% accurate" test means.

If you take the test and are healthy, there's still a 5% chance that the test will tell you that you have the disease - and that's much more likely then you actually having the disease.

There are four cases to consider:

a) you are healthy, and the test says so. p=0.999*0.95 = 0.94905
b) you are diseased, and the test says so. p=0.001*0.95 = 0.00095
c) you are healthy, but the test is wrong. p=0.999*0.05 = 0.04995
d) you are diseased, but the test is wrong. p=0.001*0.05 = 0.00005

(Sanity check: 0.94905 + 0.00095 + 0.04995 + 0.00005 = 1)

You're told that the test is positive, so you're in (b) or (c). You hope for c, of course, and the chance you're in the b group is 0.00095 / (0.00095+0.04995) = 0.01866, or about 1 in 54.

Trout

iTrader: (1)

I think you have done what the bankers and did and create the 'illusion of validity'.

If I read your answer correctly you have calculated the chances of surviving a positive test as 4.995%. Is this correct?

scud8

iTrader: (1)

I use this test interviewing for software engineering positions. Lots of people don't think about the false positive case.

Another favourite - I give you a cube of cheese and ask you to cut it into 27 smaller cubes. What's the minimum number of cuts required? You are allowed to stack the pieces any way you like for each cut.

scud8

iTrader: (1)

His answer is right. The question illustrates how what seems like a statistically fairly accurate test (95%) can give a misleading impression when applied to rare events. Even though the test is positive, it's much more likely that the test is wrong and you are healthy.

Trout

iTrader: (1)

Almost all the inaccuracy will be false positive, is it the false negative this is lost - although the test may be designed to give false positives.

Anyway - what do you think the answer is?

Dunk

iTrader: (1)

My 98% is based on:

1 / 1000 chance you'll die
50/1000 chance test is inaccurate

Therefore 49/50 chance you'll survive = 98% chance of survival following the positive test.
(Ignores the chance of a negative test result being incorrect, but it's small enough that I can't be arsed to factor it in.)

D

jods

9?
nah
6 - It's six innit

CRAP - It's not 6 -It's 4

I think

AndyC_772

iTrader: (2)

I've calculated it as approximately 1.87%. [edit: this is the chance you'll die; you're hoping to be in group c, which has a probability of 98.13%].

I always hated statistics, so I'm quite prepared to be proved wrong - but I'd be interested to know where my reasoning has broken down.

The cheese answer is 6, but it's the justification that's tricky. I consider this:

When you've finished your cuts, however you make them, you can stack the 27 smaller cubes as a 3x3x3 cube. The central cube has no external faces, so its faces must all have been made by your knife. It has six of them, so that's the minimum number of cuts you can possibly have made, however you chose to rearrange the pieces in the interim.

Trout

iTrader: (1)

The exercise is used to demonstrate how the human mind is not well designed to assess risk. It seems like a simple question and once explained the answer is simple.

Let's see if there are any more answers

scud8

iTrader: (1)

The easiest way to think of it is to consider a population of 100,000 people. 100 will have the disease and 99,900 are healthy.

- 95 of the 100 ill people will get a positive result and 5 will get a negative result.
- 94,905 of the 99,900 healthy people will get a negative result and 4995 will get a positive result.

So, of the 5090 people who got a positive result, 95 are ill and 4995 are healthy. So, if you got a positive result your chances of survival are 4995/5090 ~= 98%.

jods

It's 4 :P

stevie boy

6?

AndyC_772

iTrader: (2)

Where does the central cube get its faces from, then?

scud8

iTrader: (1)

You got the job. When can you start.

Dunk

iTrader: (1)

3


http://www.fantes.com/images/12353mezzaluna.jpg


D

Trout

iTrader: (1)

Most people give 5% as the initial answer.

The answer is actually 98% (this does not allow for a false negative).

It is a simple example but many houses of cards in banking were built on the 5% assumption - not the 98% reality!

boomer

THREE cuts???

I guess that you would call it cheating though

You would have to use a molecularly fine cheese-wire and cut down one third in and parallel to one face.

Then, as the wire got one molecule from the bottom face, move it horizontally in a further third and then pull it up cutting back to the top (in a squared U-shape).

Thus you have almost achieved the initial two cuts used in the "standard" six cuts method - bar a very thin slice/layer at the bottom.

Repeat this action (twice) in a perpendicularly way each time to divide it up into almost 27 sub-cubes.

Then wait a few seconds for the mono-molecular layers to evaporate (or something) and "hey presto" - you did it in three cuts.



mb

BOB.T

42

Trout

iTrader: (1)

How about this one.

You have a pair of old fashioned scales.

You also have a concrete lump weighing 40lbs.

You can break the lump into four pieces.

How heavy does each piece need to be to enable you to use the scales to weigh any weight from 1lb to 40lb (in 1lb increments).