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# help

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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.)

Mar 22, 2018

### 4+0 Answers

#1
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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?

Mar 22, 2018
#2
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Answer is 2/13.

Mar 23, 2018
#3
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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   Mar 23, 2018
#4
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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.

Mar 23, 2018