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If 2 cards from a standard deck are selected randomly, what is the probability that either two kings or at least 1 ace occurs? (There are 4 Aces, 4 kings and 52 total cards in a standard deck.)

Lightning  Mar 22, 2018
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4+0 Answers

 #1
avatar+560 
+1

 

Here's my work, I know it's wrong but I don't know where. 

 

There are 52 choose 2 ways to choose 2 cards, which is 1326. 

 

There are 4 choose 2 ways to get 4 kings

 

20 ways to get the aces. 

 

(20+4)/1326 = 1/221

 

This is not possible because to get one ace it is 1/13 chance. 

 

Can someone tell me what I did wrong?

supermanaccz  Mar 22, 2018
 #2
avatar+191 
+1

Answer is 2/13.

Lightning  Mar 23, 2018
 #3
avatar+85764 
+1

Probability  of   two kings  =  C(4,2) / C(52, 2)

 

Probability  of at least one ace =   1  - P (no aces)  =   1 - C(48, 2)  / C(52, 2)

 

So......total probability  is

 

[ C(4,2)/C(52, 2) ]   +  [ 1  - C(48,2)   / C(52,2)]  =    2 / 13

 

 

 

cool cool cool

CPhill  Mar 23, 2018
 #4
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0

Not quite right Phill, your probability of at least one ace 1 - P(no aces) includes two kings, so you are counting that probability twice.

Guest Mar 23, 2018

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