[hobojoe]

In Shawn's home town of Oakland, there are two cab companies - Green Cab and Blue Cab. All the Green Cab cars are painted green and all the Blue Cab cars are blue. Green Cab has 85% of all the cabs in the town. One snowy winter night a cab sideswiped another car and drove away. A witness says it was a blue cab. When tested under snowy night conditions the witness gets the colour of the cab right 80% of the time. What is the probability that the hit-and -run cab was blue?

*keep in mind, the witness gets the color of the cab right 80% of the time*

[Abhimanyu Pudi]

I think its 0.8; I don't see any hidden tricks in it.
If the witness is right, then the cab is blue. So, there is only one condition.
For the cab to be blue, witness should be right.
the witness gets the color of the cab right 80% of the time => probability = 0.8

[hobojoe]

Are you sure? I was thinking this has two parts but I just don't know how to do the second part. First, the probability that the blue car hit another without the witness would be 15%. I think there's a next step to the problem here that I just don't see with the witness involved.

[hobojoe]

Actually you may be right, maybe someone else can chime in also?

[Abhimanyu Pudi]

I think I'm right.. two conditions arise when probablity of truth or false is given instead of the given one

[Abhimanyu Pudi]

Because the cab has to be blue, the witness should be right. If he is wrong, then it couldn't have been blue cab.

[hobojoe]

It's asking whether it was a blue cab or not. Without the witness, there would be a 15 percent chance it was blue. However, with the witness, the percentage of that goes up. I was thinking it was 88 percent chance it was blue. Now, I think your answer would be right if it said, "given that the witness is correct," but it doesn't state clearly that the witness is right.

[Abhimanyu Pudi]

It doesn't state whether the witness was right or wrong, but it clearly states that the witness claims the cab to be blue.

The witness didn't say that the cab was green. If he says so, then we can consider an additional shade that "the witness was wrong and the cab is blue".

[Abhimanyu Pudi]

In Shawn's home town of Oakland, there are two cab companies - Green Cab and Blue Cab. All the Green Cab cars are painted green and all the Blue Cab cars are blue. Green Cab has 85% of all the cabs in the town. One snowy winter night a cab sideswiped another car and drove away. A WITNESS SAYS IT WAS A BLUE CAB. When tested under snowy night conditions the witness gets the color of the cab right 80% of the time. What is the probability that the hit-and -run cab was blue?

[Abhimanyu Pudi]

Any doubt? Ask me now. Don't hesitate.

[hobojoe]

I'm just trying to understand why the earlier propositions, the 85% and the 15% are irrelevant. Can you just reiterate, sorry if I'm sounding stupid

[Abhimanyu Pudi]

Sometimes, all the information given may not participate in the solution.

The conditions are:
1) the witness is right and the car is blue
2) the witness is wrong and the car is blue.

The first condition stands if the witness says it's a blue cab.
The second condition stands if the witness says it's a green cab.

You can see that the first condition is what we want because witness never said that the cab was green.
"THE WITNESS SAYS ITS A BLUE CAB".

[hobojoe]

Hm, I see what you're saying. Thanks for the help again!

[Abhimanyu Pudi]

Welcome :-)