Question 228239
When a card is selected from a standard deck of cards, find the probability of getting an ace followed by an ace without replacement


Step 1.  We note that there are 4 aces in a 52-card deck.


Step 2.  The probability of an ace in the first card is {{{P(A)=4/52=1/13}}} we call this the P(A)


Step 3.  Since there is no replacement, there are only 3 aces out of the 51 cards since we assume an ace is drawn in the first card.  Therefore, the probability of an ace on the second draw is P(B|A)={{{3/51}}}.  We call this P(B|A) where the Probability of drawing an Ace on the second draw given that Probability of A occurred or an ace was drawn on the first try.  This is also known as a conditional probability.


Step 4.  The probability is the product of the probabilities found in Steps 2 and 3.  P(A and B)=P(B|A)P(A) or P(A and B)={{{3/51*1/13=3/663}}}


Step 5.  ANSWER:  The probability of  getting an ace followed by an ace without replacement is {{{3/663}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J