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If I choose four cards from a standard 52-card deck,with replacement, what is the probability that I will end up with all four Aces?

 May 26, 2021
 #1
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Each time you draw a card you have a 4/52 chance of an ace  (or 1/13 chance)

(1/13)4 =___________

 May 26, 2021
edited by Guest  May 26, 2021
edited by Guest  May 26, 2021
 #2
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.....what is the probability that I will end up with all four Aces?      

 

By this, do you mean  

 

...probability that I will have pulled an ace each time?    

 

OR  

 

...probability that I will have pulled the ace of each suit?   

 May 26, 2021
 #3
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Good point.....questions are often unclear and subject to interpretation by the answerer.

 

If you want to get EACH of the aces it would be a little more difficult :

 

(1/52)4      

Guest May 26, 2021
 #4
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I think it would be 4/52 for the first ace, which could be any of the four aces

 

and then              3/52 for an undrawn ace, one of the remaining three  

 

and then              2/52 for one of the two remaining undrawn aces  

 

and then              1/52 for the last ace that hadn't been previously drawn  

 

for the total probability multiply them together    

 

                             4        3        2      1           24                  3   

                            ––  x  ––  x  ––  x  ––  =  ––––––––  =  ––––––––    

                            52      52     52     52       7,311,616        913,952   

Guest May 27, 2021
edited by Guest  May 27, 2021

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