Should I expect it to be a chicken or a penguin? An alien is trying to classify a group of only chickens and penguins into, well, chickens and penguins by analyzing 3 independent boolean features A, B, C.
If the animal (in reality) is a chicken, A holds for the animal 60% of the time, B holds 10% of the time, C holds 80% of the time.
If the animal is actually a penguin,  A holds for it 55% of the time, B holds for it 20% of the time, and C holds for it 90% of the time.
The alien observes an animal (that must be either a chicken or a penguin) for which A and B hold, but C is false. Is the animal most likely a chicken?
Is the answer just the greater of $0.6 * 1 + 0.1 * 1 + 0.8 * 0$ and $0.55 * 1 + 0.2 * 1 + 0.9 * 0$? Since the features are all independent?  
 A: Expanding on my comment; let's simplify. Suppose there is one Boolean variable A. Suppose that, if the animal is a chicken, A is true 60% of the time and, if the animal is a penguin, it is true 10% of the time.
Now given A, what is the probability it is a chicken?
No way to know. We could have
1000 chickens - 600 with A = 1 and 400 with A = 0
10 penguins -    10 with A = 1 and 90 with A = 0

given A = 1, the probability that it's a chicken is 600/610
or we could have
10 chickens - 6 with A = 1 and 4 with A = 0
1000 penguins - 100 with A = 1 and 900 with A = 0

Given A, then probability that it's a chicken is 6/106.
The same logic holds for the more complex case in the question. 
EDIT In the case of equal numbers of chickens and penguins (see the comment, below) it is possible to solve the entire thing analytically. Let's start simply, with my same probabilities for 1 condition: 500 chickens, 60% with A = 300 chickens with A.  500 penguins, 10% with A = 50 penguins and the chance of being a chicken given A = 300/350.
The principal is still the same for you complex case; since A, B and C are independent. We just have to figure out the number of chickens given A, B, ~C. This is 500*.60*.10*.20 = 6 chickens. Similarly the number of penguins = 500*.55*.20*.10 = 5.5 penguins and the chance of being a chicken is 6/11.5. In this particular case, we could simplify by noting that the terms for B and C multiply to the same thing for chickens and penguins, and just compare .6 to .55.
