I have came across the following question:
Two particles, each of spin 1, are at rest. It is known that the $z$ component of the spin of each is zero. Show that the probability that the total angular momentum of the system is zero is 1/3. What is the probability that the total angular momentum is $J= 1$?
I am unsure how to go about this problem as I don't know how to calculate these probabilities. Is there a trick with using $J = |l-s| , |l-s|+1, . . .,|l+s|$?