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Math Help - Independent Events

  1. #1
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    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?
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  2. #2
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    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)
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  3. #3
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    The question says that after the first number is picked, it is put aside. So that makes these two events independent, right?
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  4. #4
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    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.
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