Pre-Probability

Dan picks a random card from a standard 52 card deck. If the card’s number is a prime number, he rolls a 10 sided dice, and if not a prime number, he rolls a 6 sided dice. If Dan rolls a $4$ , what is the probability that the card he picked was prime?

If your answer is of the form $\frac{a}{b}$ , where $a$ and $b$ are coprime positive integers, enter your answer as $a+b$ .

Note - Assume the ace,kings, queens and jack cards have no number.