A building has 2 independent automatc telephone exchanges A and B. The number X of wrong connections for A in any one day is a poisson variable with parameter 0.5 and the number Y of wrong connections for B in any one day is a poisson variable with parameter 1.

Calculate in any particular day, the probability that there will be at most 3 wrong connections in the building given X≥2

I tried using P(X=2)P(Y=0)+P(X=2)P(Y=1)+P(X=3)P(Y=0) but the answer was wrong