Reposting again since my previous question may seem like it's been answered. If I shouldn't do this just let me know :)

The probability that an event A occurs is P(A) = 0.3 . The event B is independent of A, and P(B) = 0.4 . Calculate P(A or B or both occur)

According to the answers, it's supposed to be 0.58, but I don't understand how to get that. I've always thought that "or" means you add the probabilities up. So that would mean 0.4 + 0.3 + 0.4 x 0.3 = 0.82 but that obviously isn't the answer. Could someone explain how to get 0.58?

Thanks a million!

just as in a Venn diagram, it's P(A)+P(B)-P(A&B) = .70 - .12 = .58