[dfrey]

It's kind of a poorly stated problem. It would be better if they said:

1000 people were asked the question "Is this car blue?" and 900 answered yes, what is the probability that the car is blue.

or

1000 people were asked the question "What is the color of this car?" and 900 answered "blue", what is the probability that the car is blue.

The second question is far more likely to produce responses like "navy", "turquoise", etc that aren't exactly blue, but are very similar.

[munificent]

Even that doesn't fully specify the problem since we don't know the prior probability of a random car being blue. Reword the question to be "rainbow", "chartreuse" or some other less common car color and the probability should go down.

[lisper]

> we don't know the prior probability of a random car being blue

That's true, but irrelevant. The problem stipulated that this car is in fact blue, so the prior in its being blue is 1.

[munificent]

The person being asked what the probability is doesn't know the fact, so the prior probability from their perspective isn't 1.