I am trying to figure out the math to get to an answer that's given to me right away, which is $1/3$. The question is asking what the probability of $B$ is with $P(A)=0.4$ and $P(A∪B)=0.6$, with $A,B$ being independent events.

I can't seem to come to one-third? Can someone explain it to me like I'm a three year old, since I have been on this for about a few hours?

Thanks, and much appreciated! Below is the setup I keep using:

$$P(A∪B)=P(A)+P(B)-P(A∩B)$$

which, when substituting in the given values and letting $P(B) = x$, yields

$$0.6 = 0.4 + x - P(A \cap B)$$

But I don't know what $P(A \cap B)$ is, I guess $0.4x$?