I have a question about probability

Question

If there are $2$ cards, card $A$ has a light and button if press gives blue or red light with equal probability. Card $B$ has a light and button if press gives blue, red or green light with equal probability. If card $A$ and $B$ can be chosen with equal probability. What is the probability of having blue light?

Is it

$$P(\text{Blue}) = P(A) \cdot P(\text{Blue}|A) + P(B) \cdot P(\text{Blue}|B) = 1/2 \cdot 1/2 + 1/2 \cdot 1/3 = 5/12$$

Why not it is the following?

The total possible outcomes are

Blue(CardA), Red(CardA), Blue(CardB), Red(CardB), Green(CardB)

So the probability of getting blue is $2/5$.

Which answer is wrong? $5/12$ or $2/5$ and why?

Answer 1

Your second probability is wrong. Imagine you have a spinner with five equal sides labeled Blue, Blue, Red, Red, Green. In this case, the probability of landing on blue is 2/5.

Answer 2

Enumerating the possible outcomes and counting the good ones is only valid if the outcomes are equally likely, and they quite obviously aren't in your case.