I'm having problems trying to solve this question:
We have a single biased die. The probability of getting an even number as a result is three times the probability of getting an odd number. In the limit of an infinite number of trials, what is the probability of getting as result an even number MORE than half the times?
My intuition tells me that this probability is equal to 1, but I can't find a way to prove this rigorously. Thank you in advance.
In this case also the Strong Law of Large Numbers is attained: so by definition
$$\mathbb{P}[\lim_{n\to\infty}\frac{\sum_i X_i}{n}=\frac {3}{4}]=1$$