We have a credible information that a certain coin isn't symmetric. That is, the probability that we get tails is less than $0.3$.
How many tosses do we need to establish with $0.95$ certainty that the results we get will let us calculate the probability of getting tails with $0.99$ accuracy?
Here is my approach:
$p \le 0.3$ is the probability of getting tails after each toss
$X(\omega)=X_1(\omega) + ... + X_n(\omega)$ number of tails we get after $n$ tosses
$n$ is the number of tosses which we want to calculate
But I don't know how to write down the proper inequality in which I will use $0.99$ and $0.95$ which will help me calculate it.
I mean, what random variable do I need to estimate here?
Could you help me with that?