
Independent Events
I have this question  "A box contains 8 tickets 1,2,3,4,5,6,8,10. One ticket is drawn and kept aside and then the second one is drawn. Find the probability that both show even numbers."
Now I break this into two events
A = {First ticket shows even number}
B = {Second ticket shows even number}
My question is are these two events A and B independent events?

If the 1st drawn ticket is not replaced, the 2 events are negatively correlated.
If Event A occurs, the probability of Event B occuring drops.
If Event A does not occur, the probability of Event B increases.
An extreme case would be:
A = {first 3 tickets show odd number}
B = {next 3 tickets show odd number}
These 2 events are then called mutually exclusive events.
If the 1st drawn ticket is drawn and put back, then the 2 events are independent. The results of Event A has no bearing on Event B, and both could still happen, signified by P(AnB) = P(A)*P(B)

The question says that after the first number is picked, it is put aside. So that makes these two events independent, right?

I think you have misunderstood the concept of independent events.
If 1st ticket is put aside, they are NOT independent.
If 1st ticket is put back, then only they are independent.