Math puzzle

[Cyp]

90% of people will be correct about whether or not they have been abducted by aliens. 1% of people have actually been abducted by aliens.

Given the previous information, 85% of people will respond that if a person claims to have been abducted by aliens, that there is a 90% chance the person is correct, the remaining 15% of people will respond that if a person claims to have been abducted by aliens, that there is a 8⅓% chance the person is correct.

95% of people who have studied probability theory will answer correctly, and 5% of people who haven't studied probability theory will answer incorrectly. 3% of the population has studied probability theory.

Given that a person responds that there is a 8⅓% chance a potential abductee claiming to have been abducted by aliens is correct, what is the probability that the person studied probability theory?

Edit: Don't bother trying to solve this... After rereading, seems it's inconsistent...

Originally posted by Cyp
90% of people will be correct about whether or not they have been abducted by aliens. 1% of people have actually been abducted by aliens.

Given the previous information, 85% of people will respond that if a person claims to have been abducted by aliens, that there is a 90% chance the person is correct, the remaining 15% of people will respond that if a person claims to have been abducted by aliens, that there is a 8⅓% chance the person is correct.

95% of people who have studied probability theory will answer correctly, and 5% of people who haven't studied probability theory will answer incorrectly. 3% of the population has studied probability theory.

Given that a person responds that there is a 8⅓% chance a potential abductee claiming to have been abducted by aliens is correct, what is the probability that the person studied probability theory?

3%

Originally posted by Ðiscorporation
3%

am I correct or not?

[G_frog]

The first two numbers don't tell you the probability of someone who claims to have been abducted being correct. That 90% could include any fraction of the 1% abductees.

Therefore most of the statistics are useless, and the only information you have is the figure of '3%', which would be the answer.

EDIT: spent too long checking :/

Originally posted by G_frog
The first two numbers don't tell you the probability of someone who claims to have been abducted being correct. That 90% could include any fraction of the 1% abductees.

Therefore most of the statistics are useless, and the only information you have is the figure of '3%', which would be the answer.

EDIT: spent too long checking :/

\o/

"3% of the population have studied probability theory"

\o/

[Nodrog]

Originally posted by Cyp
90% of people will be correct about whether or not they have been abducted by aliens. 1% of people have actually been abducted by aliens.

It is not possible to calculate the chances of someone claiming they were abducted by aliens from this data

Originally posted by Cyp

Given the previous information, 85% of people will respond that if a person claims to have been abducted by aliens, that there is a 90% chance the person is correct, the remaining 15% of people will respond that if a person claims to have been abducted by aliens, that there is a 8⅓% chance the person is correct.

so every single person who answered 90% or 8 1/3% is wrong (ie everyone asked)

Originally posted by Cyp

95% of people who have studied probability theory will answer correctly, and 5% of people who haven't studied probability theory will answer incorrectly. 3% of the population has studied probability theory.

as noone answered correctly, none of the people asked have studied probability theory (only on average, it is possible that everyone you asked who studied probability theory was amongst the 5% that answered incorrectly, but it is statistically unlikely.)

Originally posted by Cyp

Given that a person responds that there is a 8⅓% chance a potential abductee claiming to have been abducted by aliens is correct, what is the probability that the person studied probability theory?

hence 0%, but only extrapolating from the surveyed data you currently possess rather than being an absolute probability

Cyp!

:'(

[Cyp]

Hmmm... After rereading it, think it wasn't completely consistent... Forgot to write that everything should be assumed to be uncorrelated, unless stated otherwise... Was also only supposed to be one way to work out the answer, but accidentally added enough random statistics to be able to work out two different incompatible answers... Shouldn't have added a statistic on how many people had studied probability theory...

Hadn't had much sleep, and wrote the question in a few minutes, while waiting for a train...

Sorry about that...