It's complicated, actually.

Conditional probabilities are calculated as such, via Bayes' theorem: P(A given B) = P(B given A)P(A)/P(B)

The way this is read is, "Probability of A given B," which refers to the probability of A happening, given that we already know that B happened, where A and B are some kind of event in the world.

If we assign the probabilities thusly:

A = car is blue

B = car reported blue

then,

P(A) = 0.15 (given)

P(B) = 0.15 x 0.8 + 0.85 x 0.2 (this is complicated; the terms are such that the total number of times that the car is reported blue are the proportion that are blue times the percent of times blue is correctly identified plus the proportion of green times the percent of times green is incorrectly identified)

= 0.12 plus 0.17

= 0.29

P(B|A) = 0.8 (this is the proportion of correct identifications)

Therefore,

P(A given B) = 0.8 x 0.15/0.28

= 41.4%

Alternately, we can easily do the same calculation with the green car:

A = car is green

B = car reported green

P(A) = 0.85

P(B) = 0.85 x 0.8 plus 0.15 x 0.2

= 0.68 plus 0.03

= 0.71

P(B given A) = 0.8

Therefore,

P(A given B) = 0.8 x 0.85/0.71

= 95.8%

As you can see, for the car that is predominant, there are very few errors, but for the car that is less common, the error rate is remarkably high, at greater than 50%!!! That is, don't trust your memory :)

Sorry it's so hard to read! When you try to put math symbols in, you just end up with a bunch of bold, italics and quotes.