I don’t understand how the formula for the law of large numbers will look in this question. So far I have done this:

We can say that the probability of earning 1 euro is

P(X = 1);

and the probability of losing 1 euro is equal to

P(X = -1);

We have probabilities for these two;

P(X = 1) = 19/37;

P(X = -1) = 18/37;

We can now compute the expected value of X, and since it’s a discrete variable we use the formula;

(1)*19/37+(-1)*(18/37); = 1/37

We also know that the game is played 1000 times, 365 days a year, so

1000*365; = 365000 times.

We then use the law of large numbers, which has the formula;