Let $\Omega=\{0,1\}^\infty$. For some $n$, let $B\subset \{0,1\}^n$.
I have seen these two statements which make me confused little bit.
(1) If $A\subset \Omega$, $A=B\times \{0,1\}^\infty$, and then it says that the probability of $A$ is defined as $$P(A)=|B|/2^{n}.$$
Somewhere else it says, the probability of $\sigma\in\{0,1\}^k$ is given by
$$P[\omega:(\omega_1,\omega_2,...,\omega_k)=\sigma]=1/2^k.$$
What is the connection between these two statements?
Thanks in advance