JEE Math Practice Question

Let X be a random variable such that the probability function of a distribution is given by $$P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$$. Then the mean of the distribution and P(X is positive and even) respectively are :

1. A.$${3 \over 8}$$ and $${1 \over 8}$$
2. B.$${3 \over 4}$$ and $${1 \over 8}$$
3. C.$${3 \over 4}$$ and $${1 \over 9}$$
4. D.$${3 \over 4}$$ and $${1 \over 16}$$