Probability of Two Cards Being Aces: Intro Stats Help

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In summary, the probability of at least one ace being drawn from two cards from a deck of 52 cards is 4/52 + (48/52)*(4/51).
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dherm56
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Homework Statement


Two cards are dealt from a deck of 52 cards. Find the probability that at least one of them is an ace.


The Attempt at a Solution



This is for an intro. stat class and the material is very simple but for some reason I cannot find this answer. The only attempt that makes sense to compute is (48/52)*(4/51) but this is incorrect.
 
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  • #2
Not sure why you used 48 there; change it to a 4 and it should be the correct answer.
 
  • #3
(4/52)*(4/51) is also incorrect. I used 48 the first time b/c that is all the cards besides an ace and only one needs to be drawn
 
  • #4
What is the answer?
I'm thinking you have to add the probabilities of drawing one ace and drawing two aces. Teacher didn't cover too much in probability when I studied it...
 
  • #5
Still no luck
 
  • #6
Do you have the answer?
 
  • #7
To get "at least one ace in two cards" you must either get an ace on the first card (in which case it doesn't matter what the second card is) or get a "non-ace" on the first card and an ace on the second card.

The probability that the first card is an ace is 4/52. The probability that the first card is NOT an ace is 48/52 and in that case, you still have 4 aces in the remaining 51 cards so, in this situation, the probabilty that the second card is an ace is 4/51. That is, the probability of "non-ace, ace" in that order is (48/52)(4/51).

The probability of "one or the other", that is the probability that at least one card of two is an ace, is the sum of those: 4/52+ (48/52)(4/51).
 
  • #8
That's correct, thank you very much!
 

FAQ: Probability of Two Cards Being Aces: Intro Stats Help

What is the probability of drawing two aces in a standard deck of playing cards?

The probability of drawing two aces from a standard deck of playing cards is 4/52 * 3/51 = 1/221 or approximately 0.0045.

How does the probability change if the first card drawn is an ace?

If the first card drawn is an ace, the probability of the second card being an ace decreases to 3/51 or approximately 0.0588. This is because the first ace has already been removed from the deck, leaving only 3 aces out of 51 cards.

What is the probability of drawing two aces from a deck with jokers?

Assuming the deck has two jokers, the probability of drawing two aces is 4/54 * 3/53 = 2/286 or approximately 0.0070. The presence of jokers in the deck increases the total number of cards, making it less likely to draw two aces.

How does the probability change if multiple players are drawing cards?

If multiple players are drawing cards, the probability of two aces being drawn will depend on the number of players and the number of cards being drawn by each player. The more players there are, the higher the chances of at least one player drawing two aces. However, if each player is only drawing one card, the overall probability remains the same.

Can the probability of drawing two aces ever be 0?

Technically, the probability of drawing two aces can never be exactly 0, but it can be extremely close to 0. This would only happen if there are only a few cards left in the deck and none of them are aces. As long as there are aces remaining in the deck, there is always a chance of drawing two aces.

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