Question 215375
Two cards are drawn in succession without replacement from a standard deck of 52 playing cards. What is the probability that the first card drawn was a diamond given that the second card drawn was not a diamond? (Round your answer to four decimal places.) 


Step 1.  Let P(A) be the probability of a diamond and P(B) is not a diamond or 1-P(A) for the first card.  For the first card P(A)=13/52=0.25 and P(B)=1-P(A)=0.75


Step 2.  Let Probability of a diamond occurring in the  second card given that probaility of diamond occurring in the first card be given as P(A|B)=  P(A and B)/P(B).


Step 3.  The probability of a diamond in the second card is P(A and B)=13/51.  


Step 4.  P(A|B)=P(A and B)/P(B)= (13/51)/((39/52)=0.3399


Step 5.  Answer is P(is a diamond on second card |not a diamond on first card)=P(A|B)=0.3399


I hope the above steps were helpful.


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Respectfully,
Dr J