Non-uniform distribution over a binary set

Question

Let’s consider a non-uniform distribution over ${0,1}^n$ where $0$ comes with probability $0.4$ and $1$ with probability $0.6$. If $n=5$, which is the probability of the string (for example) $11001$?

Answer 1

The answer is $$0.6^3 \times 0.4^2 = 0.03456.$$ That's because (assuming that each char value is independent from the others) the probability factorizes, e.g.

$$P(X_1 = 1, X_2 = 1,X_3 = 0,X_4 = 0,X_5 = 1) = P(X_1 = 1)P(X_2 = 1)P(X_3 = 0)P(X_4 = 0)P(X_5 = 1).$$