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Independent events in statistics

  1. Feb 25, 2010 #1
    1. The problem statement, all variables and given/known data
    Two cards are drawn from a standard deck with replacement. A=first card is an ace. B=second card is an ace. Show that A and B are independent


    2. Relevant equations
    P(A and B)=P(A given B)/P(B)
    P(A given B)=P(A)

    3. The attempt at a solution
    P(A)=4/52
    P(B) =4/52
    P(A and B)=[(4/52)(4/52)]/(4/52)=(4/52)=P(A)
    So the question I'm having is how to find P(A and B)?
    Am I correct that P(A and B)=(4/52)(4/52)?
     
  2. jcsd
  3. Feb 25, 2010 #2

    LCKurtz

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    Is your definition of independence that P(B|A) = P(B)? You have already calculated P(B) = 4/52 = 1/13.

    Now, given that A has happened, and the card has been replaced, what is P(B) then? That would give you P(B|A). If it is the same as P(B), you are done.
     
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