Question: A constructor wishes to sell 5 apartments, 3 of which in site \(\mathrm{A}\) and the other 2 in site \(\mathrm{B}\). Let \(X\) be the number of apartments of site \(\mathrm{A}\) that he will sell in the coming month, and \(Y\) be the number of apartments of site \(\mathrm{B}\) that he will sell in the coming month. An expert calculated the probability distribution of these two random variables and the following table presents his assessment:

1. What is the probability that the constructor will sell more apartments in site A than in B?
2. If we know that none of the apartments in site A were sold, what is the probability that the number of apartments sold in site \(\mathrm{B}\) is more than zero.
3. If we know that none of the apartments in site A were sold, what is the expected number of apartments sold in site B?
4. Calculate \(\rho_{I Y}\).
5. Are \(X\) and \(Y\) independent? Explain your answer.
6. Assume that the profit from selling apartment in site \(\mathrm{A}\) is 20 thousand dollars and an apartment in site B 30 thousand dollars. Denote by \(W\) the total profit of the constructor. Calculate \(E(W)\) and \(V(W)\).

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