I have just bought a deck and it has cards that have two colors within one mana symbol, like . Do I have to pay both colors or can I choose between the two?
Mana symbols such as are called a hybrid mana cost. You can pay that cost with either of the 2 colors shown. Here is a brief summary of hybrid mana rules:
Hybrid mana symbols represent a cost that can be paid with either of two colors. For example, a cost represented by the symbol can be paid with one white mana or one blue mana. It’s both a white and a blue mana symbol, and a card with in its mana cost is both white and blue.