First, we have to acknowledge that the marble draw's outcome is independent from the card being drawn. Because of this independence, we can multiply the two individual probabilities.
For the marble, there are 7 outcomes (7 marbles we could draw) and only 1 of which is checkered We have a 1/7 chance of picking a checkered marble.
For the cards, there are 5 possible outcomes (5 cards we could drawa) and 2 are prime (there are two "3" cards). We have a 2/5 chance of drawing a card with a prime number.
For the overall probability, since the two events are independent, we multiply the individual probabilities to find the overall probability:
1/7 · 2/5 = 2/35
We have a 2/35 (about 5.714%) chance of drawing a checkered marble and then picking a card with a prime number.