Probability of red ball when balls are identical

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A Bag has Ten identical Red balls and two identical blue balls. A ball is chosen randomly. Find probability that it's a Red ball.

I have confusion whether it is $\frac{1}{2}$ or $\frac{10}{12}$.

Since balls are identical is not the probability Half?

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Assume there are 1000000 red balls and 1 blue ball. Is probability 1/2 ?
Clearly $No$.

Even though the red balls are identical and so are blue balls.
It does not mean that probability is $1/2$ .

Note that the number of red balls are much larger than number of blue balls.
Hence the probability of getting red balls should be larger too.
In fact
the probability of red ball = $10/12$