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# Maths teaser( will give rep to correct answer and working) watch

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1. a criminal hides in a room with 99 innocent people. you have a lie detector that correctly classifies 95% of people. You pick someone at random, wire them up to the machine and ask them if they are a criminal. they say no but the machine goes ping and says the person is lying. What is the chance (%) that you have caught the criminal
2. This is TSR, not maths class you geek.
3. 4% that it isn't?
4. 1 criminal
5 positive results (95% accurate)

20%???????

I don't know much stats but look up Bayes' theorem
5. 80% ??

If 95% are not the criminal (95 people) then 5% have not been tested yet (i.e. 5 people)

Taking 5 people separately as 100%

Then if they were not the criminal, it would be 20% (100/5)
so therefore the remaining percentage (i.e. 80%) would be the percentage that the criminal had been caught!

or would it be 96% (i.e. the percentage accuracy of the lie detector)?
6. Its 17%
7. (Original post by Mr Einstein)
Its 17%
But why ?
8. The answer is 16.1...% I'll explain how I solved it shortly.

Edit: Explanation.

Ok guys listen up ^^ There are 100 people all together. 1 of them is the criminal. 99 are not.
The machine will test everyone.
Out of all those people only 1 will actually be the criminal. The fact that there is only 1 actually makes the calculation a little annoying.
95% of all the criminals in the room (1) will be identified correctly. Thats 0.95 of a person.

5% of all the innocent people (99) will be identified incorrectly. As the criminal. Thats 4.95 of a person.

So we have 0.95 people who are actually criminals and 4.95 who are not but they will all be identified as criminals. So what is the percentage of people who will be CORRECTLY identified as criminals?

Simply 0.95/4.95+0.95= 16.1%....

The numbers make the whole thing tricky cause of the numbers given which give you 0.95 of a human etc.
Im going to check this again and you should too, its late so i could have made a silly error but im pretty sure its right
9. i have come to the (very possibly wrong) conclusion that its 16.6667...

My logic... the lie detector it WRONG about 5 people, but if it caught the criminal it would be right so its 6/100 it could say are lying, and itll only be one of those 6 and 1/6 = 16.6667 maybe?
10. Well i think as a percentage/probability problem it should be:
possibility of the person being guilty divided by all possibilities that the lie detector will be set off
so that 1 guy x 0.95 / 99 guys 0.05% plus the 1 guy at 0.95%
therefore: 0.95/(99x0.05+0.95)=0.16101694915
which is more or less: 16.10169% that that's the guilty person

i got answer first MDMD edited his post after i posted the correct answer >.< he was wrong he origonaly said 19.19191919% (because he forgot to include the 0.95 in the denominator he just did 99x0.05 first)
not that i care or anything :P
11. (Original post by TomGB)
i got answer first MDMD edited his post after i posted the correct answer >.< he was wrong he origonaly said 19.19191919% (because he forgot to include the 0.95 in the denominator he just did 99x0.05 first)
not that i care or anything :P
12. (Original post by MDMD)
The answer is 16.1...% I'll explain how I solved it shortly.

Edit: Explanation.

Ok guys listen up ^^ There are 100 people all together. 1 of them is the criminal. 99 are not.
The machine will test everyone.
Out of all those people only 1 will actually be the criminal. The fact that there is only 1 actually makes the calculation a little annoying.
95% of all the criminals in the room (1) will be identified correctly. Thats 0.95 of a person.

5% of all the innocent people (99) will be identified incorrectly. As the criminal. Thats 4.95 of a person.

So we have 0.95 people who are actually criminals and 4.95 who are not but they will all be identified as criminals. So what is the percentage of people who will be CORRECTLY identified as criminals?

Simply 0.95/4.95+0.95= 16.1%....

The numbers make the whole thing tricky cause of the numbers given which give you 0.95 of a human etc.
Im going to check this again and you should too, its late so i could have made a silly error but im pretty sure its right
13. (Original post by Jellybean91)
Yeah, and i had 95% b4 that. Pretty sure its right now. If not, I give up. I also tried to explain the working as best as I can.
14. This thread is a geek magnet.
15. (Original post by Wilberforce)
This thread is a geek magnet.
jealous that you cant be a part of it?
16. (Original post by Wilberforce)
This thread is a geek magnet.
Btw i just saw your clone got banned. (ironic considering the thread i saw it in) You can now admit to it being you yes?
17. the answer should be 95%
because it doesnt matter how many criminals there are, when a person is picked and it is detected that the person is criminal, there's 95% of chance that the lie detector is right, so there's 95% chance that the person is a criminal.
18. another way to look at is, you pick someone at randomn (1% chance of catch) the detector has a 95% success rate (95% chance of catch) so 0.01x0.95 = .95% chance of success

which kinda makes sense, you only pick one guy and the chances of success are remote?
19. wonder if the guy who made this thread is still looking at it haha

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Updated: April 11, 2011
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