# Independent Events

• Nov 7th 2007, 08:42 AM
scw_0611
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?
• Nov 7th 2007, 08:52 AM
chopet
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)
• Nov 7th 2007, 09:03 AM
scw_0611
The question says that after the first number is picked, it is put aside. So that makes these two events independent, right?
• Nov 7th 2007, 09:39 AM
chopet
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.