How can I find the probability mass function of the following example. A pair of dice is tossed if the sum of the two outcomes is prime number the dice are tossed again and the process repeated. If the sum of the two dice is not a prime number the sum is recorded.
A. Determine the probability mass function
B. Determine the expected value for the sum
So I think my random variable $X$ has to be a non prime number. So I have
\begin{array}{|c|c|} \hline X & P(X) \\ \hline 4 & 3/36 \\ \hline 6 & 5/36 \\ \hline 8 & 5/36 \\ \hline 9 & 4/36 \\ \hline 10& 3/36 \\ \hline 12& 1/36 \\ \hline \end{array}
But I am not sure how to find the pmf
You are conditioning on the sum not being prime; in the conditional universe, all samples compatible with the conditioning event have the same relative probabilities as in the unconditional model. You calculated these probabilities for the unconditional model, now all you need is to renormalize them so that they add up to 1.
PS: From the probabilities in your question (I did not check them), the new common denominator is $3+5+5+4+3+1=21$, so in the conditional model for example $P(X=4)=3/21$ (same numerator, new denominator), etc.