Let's say that a box has a 50% chance of being selected based on it's colour and a 70% chance of being selected based on it's size. What is the overall probability of the box being selected?

Probability is not my very strong point but as far as I know, since it's a simple **and** question, you just multiply the probabilities, but then you get 0.5 \* 0.7 which is 0.35. But then it seems wrong because according to my intuition the result should be more than 0.5. So either my intuition is wrong or that I don't know how to combine the probabilities.