Random variables S and C, which can take values 0 and 1 have the following joint distribution:
Taking the marginal PMFs and then multiplying, I found out that S and C are NOT independent.
The conditional distribution $p_{S,C|T}(s,c|t)$, where T is a random variable which can take values 0 and 1, is shown below.
Taking the marginal PMFs of S and C given T and then multiplying, I found out that S and C are conditionally independent given T.
My question is: Is it possible to find the probability that T is zero or T is 1 from the tables above?
From Baye's Rule, $$p_T=\frac{p_{T\mid S,C}\cdot p_{S,C}}{p_{S,C\mid T}}$$ however $p_{T\mid S,C}$ is not known. Any idea?