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Grind

Probability

I'm reading a book on chance and probability and this one was a little bit counter-intuitive until you do the sums.

There are two colours of taxis in town. 85% are green and 15% are blue.

A woman hails a cab at random.

Independent testing suggests that she is able to remember the right colour 80% of the time.

After getting home, she tells you the taxi she hailed was blue.

Should you believe her?

* and who paid for the taxi *
Pond Life

Yes i believe her. I'm trusting like that. I have no idea why she would lie to me about the colour of the taxi.
Grind

Pond Life wrote:
Yes i believe her. I'm trusting like that. I have no idea why she would lie to me about the colour of the taxi.


She's been out and smells a little like Bailey's?
Pond Life

That sounds revolting.
Grind

It's most likely to be green (59% likely).

Basically, if the bint claims it is blue then........

The probablity of it being blue is 0.8x0.15 = 0.12

The probablity of it being green is 0.2x0.85 = 0.17

It is therefore likely to be blue at 0.12/(0.12+0.17)=0.41 (or 41%).

Which logically means it is probably green.

Daft bint.
Grind

Grind wrote:
It's most likely to be green (59% likely).

Basically, if the bint claims it is blue then........

The probablity of it being blue is 0.8x0.15 = 0.12

The probablity of it being green is 0.2x0.85 = 0.17

It is therefore likely to be blue at 0.12/(0.12+0.17)=0.41 (or 41%).

Which logically means it is probably green.

Daft bint.


If she were to claim it was green, she'd be in much better shape:-

Probablility of green = 0.8x0.85=0.68

Probability of blue = 0.2x0.15=0.03

Which suggests it should actually be green 0.68/(0.68+0.03)=0.96 (or 96%).

How dull is this?  
Grind

Clacker wrote:
*Nods off*


Taxi for Mr Clacker!
Grind

Daft mare got a free lift home with her new "friend" anyway.

Probably.
Grind

Clacker wrote:
Grind wrote:
Daft mare got a free lift home with her new "friend" anyway.

Probably.


I feel like I've just sat one of those multiple-choice exams where you just guess the answer and pray.


Well, if you guessed green, you were in pretty good shape whatever.  

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