A coin probability question Let $p$, $q$ be values in $[0,1]$ and $\alpha \in [0,1]$. Assume $\alpha$ and $q$ known, and that $p$ is unknown parameter we would like to estimate. A coin is tossed n times, resulting in the sequence of zero one valued random variables $X_1, X_2,...X_N$. At each toss, independently of all other tosses, the coin has probability $p$ of success with probability $\alpha$, and probability $q$ of success with probability $1-\alpha$.
I just wrote down the background where I have confusion. The problem requires to find MLE of $p$ which I know how to do once I understand the background. I have trouble understanding this problem, especially the bolded line. What does it mean?
 A: Let's have three biased coins. Coin $A$ produces heads with probability $\alpha$, coin $B$ produces heads with probability $p$ and coin $C$ produces heads with probability $q$.
Here is the experiment: We flip coin $A$. If the result is heads then we flip coin $B$ otherwise we flip coin $C$. The result of the experiment is the result of the second flip.
We can perform a long series of the experiments described above. So, we can estimate the probability of heads as results.
The probability that the result of the experiment (the second flip!) is heads is
$$\pi=P(\text{heads})=P(\text{heads}\mid \text{ coin } A \text{ is tossed})\alpha+P(\text{heads}\mid \text{ coin } B \text{ is tossed})(1-\alpha)=$$$$=p\alpha+q(1-\alpha).$$
So $\tilde{\pi}$, the relative frequency of heads can be estimated experimentally, that is the probability of heads, $\pi$, can be considered to be given after a while, and then, we have the following equation for $p$:
$$\tilde{\pi}=p\alpha+q(1-\alpha).$$
$p$ can be determined:
$$p=\frac{\tilde{\pi}-q(1-\alpha)}{\alpha}.$$
