Taken for a ride

[The Magic Pudding]

Out of 100 cars, 85 of which are actually red, 15 of which are actually crimson, you would identify more crimson cars than you actually saw: 20% of the 85 red cabs you saw you would mis-identify as crimson, if I'm reading this correctly, which means you would identify 32 cars as crimson, only 15 of which actually were crimson.  17 would be red.  So there is a slight chance in favor of the cab actually being red.  That's my stab in the dark.

D'accord.

D'accord?

All these questions where the obvious isn't correct, sewing discord in our brains and then you throw one in where the obvious is the answer.  Bastard.  

[Steve Reason]

I have a headache now. 

[En_Route]

Where I live there are two taxi firms, Red Cabs which have 85% of taxis on the road and Crimson Cabs which have the other 15%. Both firms'  taxis sport the colour of their  owners. Last night I saw a cab crash and identified it as a Crimson taxi. However, my vision is not wholly reliable at night; I can be expected to correctly identify a crimson taxi 80% of the time; the other 20% of the time I will mistake a red taxi for a crimson taxi. Was the taxi I saw more likely to have been crimson or red

Out of 100 cars, 85 of which are actually red, 15 of which are actually crimson, you would identify more crimson cars than you actually saw: 20% of the 85 red cabs you saw you would mis-identify as crimson, if I'm reading this correctly, which means you would identify 32 cars as crimson, only 15 of which actually were crimson.  17 would be red.  So there is a slight chance in favor of the cab actually being red.  That's my stab in the dark.

D'accord.

So that is the correct answer?

But I don't understand.

You stated
"I can be expected to correctly identify a crimson taxi 80% of the time; the other 20% of the time I will mistake a red taxi for a crimson taxi."
But you haven't stated that you mistake red taxis 20% of the time for crimson.

The first part of above
"I can be expected to correctly identify a crimson taxi 80% of the time;"
This could be either
1. out of all the crimson taxis that pass you by, you only recognise 80% of them as crimson
or
2. out of all the crimson taxis that you recognise only 80% of them are actually crimson

But when you state 
"the other 20% of the time I will mistake a red taxi for a crimson taxi"
"...the other..." implies option 2 from above.


If The Black Jester's statement was correct then of the 100 taxis 85 which are red and 15 which are crimson, you see 32 crimson cars, 17 which are actually red and 15 which are actually crimson.
However, how does this fit with your statement "I can be expected to correctly identify a crimson taxi 80% of the time;"
In TBJs answer you are only correctly identifying a crimson taxi 46.9% of the time, not 80% of the time.

The inference is in fact that I  mistake red taxis 20% of the time for crimson,but my wording was sloppy. I therefore declare all answers correct.

[Stevil]

The inference is in fact that I  mistake red taxis 20% of the time for crimson,but my wording was sloppy. I therefore declare all answers correct.

Yay, I thought I was missing something simple here.

[Stevil]

BTW, thanks En Route, this stuff is fun,

Takes me back a few years, probably 13 year or 14 year old math????
Helps to de-mush the brain.