SOLUTION: Two cards dealt from an ordinary playing deck. Find the probability that the second card dealt is a heart.

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Question 1183530: Two cards dealt from an ordinary playing deck. Find the probability that the
second card dealt is a heart.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


The probability is the sum of two mutually-exclusive possible outcomes:



P = P(heart on first draw) * P(heart on 2nd draw) +

    P(non-heart on first draw) * P(heart on 2nd draw)



P = (13/52)(12/51) + (39/52)(13/51) 



You can do the calculations to get 1/4.



This makes sense qualitatively, if you think about it.



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EDIT: There is an old version of this problem answered by Theo.  Theo's answer is very confusing and incorrect (he mistakenly substitutes "red" for "heart" in his early calculations and erroneously comes up with a final answer of 1/2).   



There is also an older version of this problem CORRECTLY ANSWERED by tutor Edwin.