How are event probabilities computed from outcome probabilities?

"The easiest way to think about probability measures is to start with the probabilities of the outcomes, not events. Each outcome has a specific probability of occurring. The probabilities of events logically flow from that just by using addition. For example, imagine that Fox Broadcasting is producing a worldwide television event called All-time Idol, in which the yearly winners of American Idol throughout its history all compete against each other. The four contestants, along with their probabilities of winning, are Kelly Clarkson (.2), Fantasia Barrino (.2), Carrie Underwood (.1), and David Cook (.5). Computing the probability for a specific event is just a matter of adding up the probabilities of its outcomes. Define F as the event that a woman wins the competition. Clearly Pr(F) = .5, since Pr({Kelly}) = .2, Pr({Fantasia}) = .2, and Pr({Carrie}) = .1. If P is the event that a rock singer wins, Pr(P) = .7, since this is the sum of Kelly’s and David’s probabilities."