Probability of an event happening if at least one of 2 events happen So I'm doing a probability question, the probability of event A happening is $0.4$, event B is $0.7$. What is the probability of only event A happening given that at least one of the two events happen?
What I have tried so far is getting the probability of at least one of two events happening, which I got $0.82$ from adding the two and subtracting their sum. From here I'm not too sure where to go, I have thought about the simple operations I could do such as multiplying the $0.82$ by the probability of the $2$, but none of them seem to be the right choice.
EDIT: sorry I forgot to mention that it's given that these two events are independent 

You want to find $P(A \cap \neg B|A \cup B)$.
$$P(A \cap \neg B|A \cup B) = \frac{P((A \cap \neg B) \cap (A \cup B))}{P(A \cup B)} = \frac{P(A \cap \neg B)}{P(A \cup B)} = \frac{P(A) P(\neg B)}{P(A \cup B)} = \frac{P(A) P(\neg B)}{1-P(\neg A)P(\neg B)} = \frac{0.4 \times 0.3}{1-0.6 \times 0.3} = \frac{0.12}{0.82} \approx 0.146$$
I think is helps to look at these problems visually too. Since the two events are independent we can draw the event space to look like the following picture (imagine you can take a horizontal line to sample the event space):

