Possible Duplicate:
Probability of two opposite events
Suppose there is string of eight bits, e.g.:
00100110
Bits are randomly chosen from the string. Location of bit (in the string) does not influence its selection probability.
Probability of choosing $0$: $p_0 = \frac{5}{8} = 0.625$
Prob. of choosing $1$: $p_1 = \frac{3}{8} = 0.375$
Suppose there is an ongoing process of selecting $0$ and 1. So at each moment, $0$ or 1 is selected, and represents current state C of the process.
Probability of choosing opposite state (to current state C), and then again opposite state – such complex event is called cycle – is given with:
$p_\text{cycle} = p_0 \cdot p_1 \space\space\space (1)$
Question: define $p_a = p_{cycle}$. Then, opposite event is $p_b = 1 - p_{cycle}$. We have again two opposite events. How will the $p_b$ look like? I.e. what sequences of $0$ and $1$ will belong to events of kind A and events of kind B. I have problem defining B-set.